I have either a Trijicon Mini Reflex, Burris Fast Fire II or a Micro Aimpoint on my shotguns. Dont recommend the Trijicon. Doctor Optic/J point/ Fastfires make a nice small compact red dot site. The aimpoint Micro H1 is a good choice. You will probably need a picatinny rail for most of the good stuff, although some of the mini stuff has proprietary mounts that you can get.
Have you considered a Wilson ghost ring site set instead?