It seems like you are trying to recruit new members to your church, right?
If you are extending the invitation to people in general (like strangers, passerbys, etc), why don't you just print up some invitations/flyers...I'm not talking religious tracts, but some sort of note with a description of your church/location/pastor/message...like a message that there is a new congregation in town. If you see a friendly face in the supermarket, library, mall whatever, just say "Hello, if you are interested in a church home, check us out!"..smile, and keep it moving.
I don't think this is tacky at all. I've received many church invitations this way. I think the only thing that is tacky is if you harass folks to come to your church lol, but I doubt you would do that!