We are a bit fussy here at work, but lots of people use small french presses. Bodum I think makes the 12 OZ that I use. I forget the model. There are also gravity systems like the one I use for tea (Bonjour / available at Teavanna) that should work for a ground coffee. They clean easy, too - just pore some water in, take it over to the toilet, and dump the water and grounds out. That'll do.
Alternatively, one thing I do for tea is keep an old plastic 1 qt container as kind of a knock out box for tea leaves. You could do the same for grounds. I keep dishwashing soap around and clean out my tea stuff good in the morning.