I'm assuming the back has what look like cushions, they are just attached. If you have the sewing talent to make a piece that fits over the front and sides and overlaps onto the back just a tiny bit you could hand sew it to the old cover with a leather needle.
Seems like there should be another way tho. I just did a search on vinyl repair and found this stuff that claims to repair the tear not matter how large. You might check it out and read the reviews.
Good luck.
Kathy

Here is a link that might be useful: Liquid stitch

are they like the repair kits at auto-supply stores? they have good ones there with matching grain ironing pads...
maybe you can post photo of sofa and damage...to see where seams are,how big a tear...

hope you can find a solution!
kudzu

We got a couple of the auto repair kits, but they're really for something a lot smaller than the damaged area and just didn't work. This is the cushion. (I wish the cushions were removable...I'd just flip it over! lol)

The damaged area:
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This was an attempt to fix it using the repair kit. The adhesive didn't even hold 48hrs. and it started turning loose and the glue turned into a powder like stuff.
{{gwi:1476649}}