Well if your Just looking for Ideas for the Omni system and also Colecovision here's a bunch.
Good luck with your Omni system. Lots of potential for some new old school games.
Mr. Do - A nice Arcade port of the first Mr. Do. Lets face it the Colecovision port of Mr. Do isn't the greatest, but it's the best version of the time.
Boulder Dash - The MSX and Commadore 64 versions are superior to the Colecovision version. You could even add more levels.
Jumpman - Colecovision has Jumpman Jr. and there was also the actual Jumpman game. Maybe a port of Jumpman with new stuff or a totally new game.
Dragon Warrior - A Randomized game from what the Nes version has. Or even a new RPG that functions something like Dragon Warrior 1 - 4. Your own graphics and IP.
Bubble Bobble - The MSX version is ok at best. If it was more like the Nes version with Randomized levels it would be fun. Maybe some type of new mechanic or even custom graphics so you could make your own IP.
Castlevania - A totally new castlevania game with your cool looking engine. All new levels, maybe add in whip angles, and possibly more playable characters. Or even your own graphics and IP.
A beat em up game - Something along the lines of Mighty Final Fight or River City Ransom. Your own graphics and IP.
A generic wrestling game - Your own graphics and IP.
Donkey Kong 3 - Your own graphics and IP because the big N would say no.
Donkey Kong - You have the engine programmed. Why not keep the mechanics and make it a totally new game that's your own. New levels and graphics and your own IP. Heck you could use the same graphics from the above suggestion.
Donkey Kong Jr. - Make it your own using the same game mechanics with all new levels using the graphics from above two suggestions. Now you got yourself a Trilogy. Ha.
Some type of space shooter. - Something with some complexity like Solaris on Atari has. But maybe have some alternating play styles to what Solaris, Starwars on Coleco, and R-type had to mix everything up. Obviously your own graphics and IP.
Dig Dug Style - Will need some good thought to pre laid out levels. No Digging. Only up/down lanes that are pre setup with quick enemies. Enemies can change lanes. Can only walk and shoot up/down. Jump to the left and right lane are buttons 1 and 2. Button 3 shoots. Obviously your own graphics and IP.