Well if you are looking for nitrogen and don't want to put much tword fertilizing it, I'd recomend a legume crop (make sure to get the appropriate innoculant to go with em though.) I'm not sure how many times a year you can mow it but alfalfa is a great one. At least alfalfa hay is a good green. Try checking with seed companies for cover crop ideas for your climate/conditions. Clovers are another one. Peas, beans, and vetch are all legumes I've heard of people using for cover crops.

Other plants I've heard of that can provide good boosts to compost include comfrey and yarrow. Comfrey isn't really a cover crop type plant though, it is one I've only planted a few months ago but you want to place this herp in a location that it can stay. Aparently trying to iradicate comfrey once it is established can be difficult. Anyway, I've heard that 7 comfrey plants is enough to keep a good supply of green manure on hand. I don't know how realistic that is but it looks like a nice enough plant to me and is good for healing if you are into that sort of thing.

As for yarrow, depending on the variety, it can really become a weed so you may have plenty of it for your compost.

Grass can be a wonderful source of nitrogen for your compost as well. If you already have grass growing in that area, you might just mow and use the clipping for your compost.

Look around at what seems to grow like weeds in your soil, those plants may just be a perfect thing for your compost.

Good luck

Alfalfa is tops. Rodale did tests years ago and alfalfa was 3 to 4 time the natural nitrogen producer of any other plant tested. Other legumes that did well were white and red clover and vetch. There are a few others. I find it's hard to find alfalfa seed from normal retail sources, so I get mine from a local farmer who is glad to give me all the little bit of seed I need in exchange for some nice tangerines and some dates we grow. There are a lot of deferent varieties of alfalfa. Be sure to get one that does well in your area and takes lots of cutting. The local ag. agent can help you with selecting a variety. But even if you can't get the perfect variety, most any variety that grows in your are will do fine.
Be sure not to cut alfalfa to short. It's not like grass. A mature stand needs a fairly good stalk above ground to sprout back from when cut.
I live in a very different climate. I grow mine from fall to spring. I mix alfalfa and winter rye seed about 1 part alfalfa to 3 parts rye by weight. that is about equal parts by seed count. I scratch these in about double thick because I have a HUGE number of quail and dove come in and feast on my seed, and then the fresh tender greens. I have seen as many as 8 covey of quail, each 10 to 15 in number and 300 dove on our tiny little 1 acre date garden. Well, its small when you put 400 birds on it at once. but the quail also scratch for bugs so they are doing their part to help clean up and keep bug out. A little trick to keep them from eating too much from the field so that they don't make bald spots. I put some cracked corn or chicken scratch at the ends of the field so they eat that and leave my planted seed alone.
As summer stats warming up I let it go to seed then cut it all to the ground and rake it into windrows as part of the mulch beds.
this is what my roes look like. you can do adjust it on a small scale.

mmTmmCCCCCmmTmmCCCCCmmTmm

Were T is a tree or a date palm, m is mulch beds, and C is orchard crop. In most cases the orchard crop is rye and alfalfa mix, although I do use selected native weeds too. Notice I said selected! local weeds. Lambs quarter, goat nut, are good greens for salad, and a couple of local flowering or fragrant beauties, dye weed (perennial legume), verbena, and desert primrose. Yes we have a native primrose out here in the crazzy hot desert! It doesn't grow every year, only grows when the rain is just right. But I digress.

Some folks like to keep a more perennial crop like alfalfa alone of vetch so they don't need to reseed each year. With alfalfa, if you want it to carry over and grow the next year, you need to leave some leaf and green as winter starts, and not cut it all off.

Note too, that after 3 years of heavy mulching (say one foot thick or more) you will be able to reduce the amount to half as much, as your soil will have matured and developed a very healthy profile.

Where in Michigan are you? What kind of soil do you have? What is the humus level of the soil you have? What is the soil pH?
Getting Alfalfa established can take time, depending on your soil and its pH, and the soils nutrient load, although that is a good, sustainable, source of organic matter. Around here getting a stand of Alfalfa establihed in this Lake Michigan beach sand can be difficult unless the soil is first well amended with organic matter and dolomitic limestone is applied to correct the Magnesium deficiency that is common here. There are however stands of Alfalfa that have been there for years and are doing really well even today, with proper care of the soil.

This won't help for all year, but if you need greens in the autumn when all the leaves fall, grow asparagus. This year I cut down my stalks and shredded them alternately with leaves and the pile really heated up. The stalks stay green even after several hard frosts.

How about Swiss Chard? Easy to grow; easy to eradicate if you change your mind. Grows from spring all the way through the summer to hard frost. Eat what you want and harvest the rest for compost greens. It grows back repeatedly. Bonus: the roots get huge & can be left to rot over the winter, loosening the soil. On a much smaller scale, this is what I do.

Thanks everyone for the input. The comfrey is an interesting suggestion. My dad grew it many years ago, made tea with it and if memory serves me right, fed it to the rabbits and goats.
I will probably experiment with the alfalfa next spring.
Kimmsr - I am more or less midwest MI, Holland area. I have sandy soil with what I think a good content of organic material. I add leaves, compost and a cover crop of cereal rye almost every year. I don't get to scientific with soil tests, PH or such but my veggies and perennials are as good and healthy as any. My biggest problem is not getting enough sun, the trees have grown up around my little plot and I haven't the heart to cut them down.
Thanks again...Old Dirt...

You are just down the road apiece. I have the same soil as you, that nice fluffy Lake Michigan beach sand as do most of the farms around me. Many do have a good stand of Alfalfa but it takes work. My place, oldtimers tell me, once grew Timothy hay for the Muskegon market and that is all that is wrong with my soil, it was Timothied to death, nothing was ever put back into the soil, it was just tilled and planted and harvested and all of what the land produced was taken off and nothing was ever put back, not even manure.
Talk with the people at your Michigan State University USDA Cooperative Extension Service Ottawa County office because they will know about getting Alfalfa established on your sand as well as the clay that you also have further inland. Jim Veldheer (Veldheer's Bulbs mixes lots of horse manure and leaves into the sand he works to grow the spring flowering bulbs he sells down there. But he also has soil tests done by the MSUCES.