That will work. Put newspaper or card board down and then the grass or leaves. This fall begin collecting leaves. Yours and any others you can find.
If you have access to shredded paper, that will work also and feed the worms.
Do not use week block are any plastic, as that heats th soil too much.

Grass clippings will contain a lot of seeds from the grass, especially if it is Bermuda. As plantmaven said, put down a barrier first so the seeds will be able to sprout, but not root. We use grass clippings to quickly fill in a bare spot in the yard.

Exactly what Plantmaven said.

Molly

But if i put down newspaper ( not dealing with carboard again-had it under the soil and turned into a nightmare) wouldnt it become a messy mush with the watering system? Plus, the ink would leach into the soil...

The paper will decompose and feed your soil.