Add rabbits. Wild rabbits look after themselves (no need to cage them or anything), and will keep grass down to a height of about 2 inches.

They stay within about 50 yards of wherever their 'home' hole is, so they won't run off (although their offspring may!).

You still need to mow about twice a year to get rid of plants the rabbits don't like to eat, which will otherwise grow into bushes.