The rivets must come out! I recently changed one of those ring-gears. I had no problem getting the rivets out. They aren't taperred! And the new bolts worked slick as a whistle!
As for the magnet, if you just broke it a little, or it is an one or two pieces, work with it, get it back in as good condition as you can, clean the place where it goes, and glue it back on with JB WELD, a really good "stickum" for the job. Note: Carefully mark the side of the flywheel where the magnet was, BEFORE cleaning it up! If too badly deformed, check with a lawn mower repair shop, to see if they might have an old flywheel lying around, that you might get a magnet from.

Good advise from rusty. Yes, supporting the flywheel they will drive out easily. I just take an abrasive disc and lop the rivet off through the plastic gear- then drive the rivets through. Quick and easy...

Thank you for all your advice, I really appreciate it. The magnet is missing a little piece on the corner. I have it and actually thought I would crazy glue it back on since the magnet itself is keeping it together.
I didn't work on it today, but tomorrow I'm gonna get back to it, now that I know it's ok to pound the rivets hard without hurting anything.
Here's another question for ya's...... if I keep shearing off keys when I start it up, does that mean that I don't have it torqued enough? My brother said that you can't over torque it (without snapping the bolt, of course), is that true? I looked online the last time I had this dang thing apart, to see what it should be torqued at, and did as it was posted, but the key sheared off again. Any suggestions?

***"I looked online the last time I had this dang thing apart, to see what it should be torqued at, and did as it was posted, but the key sheared off again. Any suggestions?"*** Does that mean you asked for advice from one of them dang forums, or what?? Seriously, are you using a torque wrench? I know everybody does not have a torque wrench (but I still don't understand why not). One old time mechanic said, "Boy, don't believe all that stuff when people tell you they don't need a torque wrench. They are the ones that always want to borrow your "EZ Outs" when they break off a bolt, and they want you to tell 'em why their head gasket came back leaking too."
Make sure you clean off all traces of oil or dirt from the mating tapers of the crankshaft and the flywheel before tightening and torquing it down. There must be a good, clean, "metal to metal" fit between the two components to keep the flywheel secure.
I might ask, before the ring gear "went south", had you been having any other problems in starting? Any "half turn of the engine and stop" events??

Yes I do have a torque wrench and used it the last time I had this apart. I did have problems with it starting, but it was the starter wheel that went that time (both wheels were plastic). But other than that, no problems with it.
Probably the only thing I didn't do was make sure that there were no traces of oil on the taper. I will make sure I clean it well tomorrow. Do I need to go as far as cleaning it with alcohol?
Thank you!! :)

Actually, a little clean solvent on a paper towel will do. Lacquer thinner, mineral spirits, acetone (nail polish remover), or spray carb cleaner are all suitable. And it only takes a bit on the towel or rag. Do not spray or douse the crankshaft, you could harm the seal. The reason I mention it at all is because I have seen/heard other people "coat" the mating tapers with lube grease, oil, or anti-seize compound before mating them up. That's a no no.

THANK YOU SO MUCH!!

QUESTION
If you are changing a plastic ring gear with an
aluminum gear Don't you also have to change the
starter pinion from metal to Plastic?

I found it difficult to punch out the rivets, I started
with a large center tipped drift and wound up using a
drill bit to hit the pin out.

I also broke a magnet, but declined gluing it back as
I thought a LOOSE MAGNET would wind up destroying the
fragile alternator coils. NO VIBRATION

I found that when torquing down the bolt/nut and waiting
that the pressure drifts down as the softer key gives.
A re torquing showed 30 Pounds slip. Also if you start the
motor (10 sec run) you will find the torque to slip.
That may be why keys are sheering.

***"the pressure drifts down as the softer key gives."***
NO! If the correct key is used, along with the CORRECT installation technique (for putting the key into the keyway), there will be no additional settling of the flywheel, after torquing the fastener. Nor will there be any "give" of the "softer key". If you are realizing the results you cite above, there is something amiss in your procedure for situating the key into the keyway. From what you are describing (drift, give, loss of initial torque), I believe you have been trying to put the key into the crankshaft keyway, with the upper end of the key COMPLETELY flush with, or BELOW, the upper end of the keyway slot, and then trying to lower the flywheel onto the crankshaft. If this has been your method, you need to change it a bit. The technique I was taught, was to set the flywheel onto the crankshaft with the mating keyways in as close alignment as possible. Next, insert the key into the keyways (you might have to raise up one side of the flywheel or jiggle it a bit to get the key started into the keyways). Once you have the key started in the keyways, push down on the flywheel to assure it is seated squarely and completely on the crankshaft taper. Now, you can gently tap the key into the keyways until the upper end of the key is just flush with the upper surface of the flywheel mounting hole/keyway. DO NOT beat on the key and/or flywheel after the key has been "teased" into this position. Any further tapping or beating could cause the flywheel to move, allowing the key to move deeper into the keyway, which will cause the flywheel to climb upward on the taper, resulting in the things you describe above.
The key (when properly situated) does not crush, settle, or give. There is no clamping force applied to the key or any portion of either keyway. All the clamping and gripping force is meant to be applied ONLY to the mating tapers, the threads of the crankshaft, and the top surface of the flywheel. Good that you mentioned this. That's one drawback of long distance repair work, we can't look over your shoulder to see what you're doing.

I got your lesson.
I have been doing it the wrong way that
you mentioned. Add to that, the use of a non
approved B&S key and I can see why I get the
torque drift.
It is nice to get taught something that you
experts take for granted.
I think I may get the wife off the mower and
take the motor apart and try out your technique.
\Oh hell, I'll just wait for a day or two and she
will lower the deck and hit a root and I will need to take
it apart anyway.

"I found that when torquing down the bolt/nut and waiting
that the pressure drifts down as the softer key gives."

Agree with mownie on this.

I once asked an old time mower repairman what he was using for a torque wrench when I didn't see one. He said his false teeth, startled, I said false teeth? Yah, he said, when they grit, I quit tightening. Course, this was the same guy who kept a broken engine crankshaft hanging over his work bench to remind himself TO use a torque wrench.

Walt Conner

***"Oh hell, I'll just wait for a day or two and she
will lower the deck and hit a root and I will need to take
it apart anyway."***
OH NO! You don't realize it but you just sent ole Murphy an early wake up call. You better get out there and chain the deck up to the frame so it can't be lowered too far.

I just had to leave one more message for all of you who answered my question. My husband and I put the mower back together today and it's running the best it EVER has!!

I took a dremel tool with a cut off blade and cut the rivets off and then punched them out with a punch (was easy really). Then we took steel wool to all of the magnets and shafts and then hit them all with a towel that had alcohol on it. My husband took the dremel tool with a very fine ginding stone to the coil "thingys" and then wiped them down also with the alcohol towel (we also took an air hose to everything after sanding or using the steel wool, just to get every little spec off, before using the alcohol). Then, we made sure the shafts were perfectly aligned and then tapped in the key until it was level with the flywheel. We then torqued the bolt to the specs that came with the aluminum flywheel gear.

It was an easy job to do IF you have the proper tools.
Thanks for all of your responses, you all helped us tremendously!! Thank you again!

FORGOT TO TELL YOU........Our mower hadn't been ran since last fall (when it broke down) and when we first started it today after fixing it, it did not hesitate ONE BIT! It just started and ran beautifully! NOR did it skip AT ALL while my husband was mowing the lawn.
I have to say that this is one "do-it-yourself" job that is totally satisfying for me! I am proud!! :)