If you put manure on a tarp for 9 months, several things will happen. 1) weeds and grass roots will invade the manure and establish themselves. 2) the tarp will rot and you won't be able to get it back out. 3) and therefore you will have tiny blue streamers of tarp decorating your garden soil in perpetuity, AND larger pieces that make planting difficult and tilling hazardous. Also I would not count on it to totally kill the grass.
I have done a fair bit of this sort of thing, tried lots of different methods, here are the three no-dig-no-till methods I've found to work best for me:
1) best is to solarize the area ALL SUMMER, correctly (meaning, scalp the grass to the ground first with mower or weedwhacker, then cover with clear plastic and seal edges very well, weighing down with a few boards across the middle if necessary to keep it from flapping away); at the end of the summer, remove plastic, cover with layer of newspapers or cardboard and then top with manure, compost or mulch; then dig in or till the next spring and away you go.
2) you can skip the solarizing if you want, especially if you don't have too-awful perennial-rooted spreading weeds to deal with. Don't skip scalping it down or covering with cardboard though.
3) or, for slower but low work input, get some large discarded carpeting from the curbside on garbage day, put it upside-down on the area after scalping the grass back, ideally cover the upside-down carpeting with some mulch or straw (NOT manure or compost), then leave it alone for a year or two. It'll be really nice when you finally drag the carpet back off it; and the carpet can often be reused several times, depending on its quality.
Good luck, have fun,
Pat
. I didn't have much success with cardboard, I'd probably go with plastic and *bake* it until it's all dead. It'll be back soon enough anyway! -Wendy
