Sidescrolling games like Flappy Birds where the character moves by themselves can be fun. 3D based sidescroller games like Temple Run, and Subway surfer are okay games where I can also move left, right, and jump.
Have you tried Legacy of Discord? there's a same way where you have the option for "auto" or "stop auto", it's kind of fun especially if you have to do some chores you can just leave it for a while completely. Yeah Subway surfer is fun, I have it on my ipad it's kind of a timing game