At Accessibility Summit in March my husband Lee and I spoke on outreach events for families with disabilities. During the Q & A time we talked about activities specifically for teens/adults with disabilities (including those living in group homes). Here are some ideas we came up with after the discussion and as we've been talking about it in the weeks since then:
Coffee shop with praise band - One disability coordinator who attended our session said on the night the praise team practices, they set up a coffee shop concert-like atmosphere and the older teens and adults in their church with disabilities are the audience. The band loves having people to play for and those who attend are free to move around and enjoy the music without the formality of the Sunday morning service.
Square dance - If the teens and adults in your church enjoy the Tebow Night to Shine prom, maybe they would enjoy getting together more often for dancing and socializing.
Walking club/exercise class - It would be great to explore you area together as a walking club that meets at different state parks or walking trails. If that isn't an option where you live, an exercise class would also be fun. My older sister (who has Down syndrome) goes to an exercise class at her church twice a week and loves it.
Game night - It could include dominoes, bingo, board games, or even X Box games set up to play together.
Sporting events - The adults at your church may enjoy getting together for a baseball game or other sporting event. We live near Houston, so we have lots of opportunities, but even when we lived near the smaller town of York, PA, we enjoyed going to York Revolution games, a smaller league team.