Some times a large church will set up its own league and will organize it's members into teams. Most of the time church leagues are set up so each team represents a church and churches may have more than one team.
The church league that I'm most familiar with was started in 1941 by four churches that had decided that duck pin bowling would be a good to encourage friendship between Christians of different denominations. The league reached a peak of about 16 five man teams representing about 12 churches. Most of the churches were in Norwalk, with one from Darien and a couple from Wilton.
The connections between the teams and their churches has faded over time. In the 1980s when one team brought the championship trophy to church the Sunday after the banquet, the minister's reaction was a shocked, "We have a bowling team?" We are now at the point where several teams have no church connection at all.
I think the place to start would be to contact the pastors of the local churches and at least some of the church council members (Deacons or trustees) and let them figure out what day works best.
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