You're just going to have to be honest. Just tell your neighbor that you're sorry, but you are not going to be able to help them out. You are not really interested in being their regular babysitter. If there's an extreme emergency, you hope he knows he can count on you, but unless it's an emergency, they're going to have to find someone else.
This has happened to me several times, since I don't have a job outside my home. I have found that there's only ONE explanation people are willing to accept when I tell them I can't/won't babysit. And that's the "Because I don't want to" reason. Simply put, you can't babysit because you don't want to be a babysitter. Anyone who would argue with you about it isn't worth worrying about their friendship over, IMO.
I agree with Shoo, completely and totally.
Nothing good will come from saying things like "We're not comfortable doing overnights" because then they will expect you to babysit during the day and you don't really want that.
You need to make clear in a friendly way that you are simply not in the babysitting business and will not continue to babysit these children under any circumstances other than a real emergency.
I think I do, too. It's just a weird situation. I really like neighbor, and he has done some helpful things for us.. he has lent us tools, brings us vegetables, even caught our cat when he got out unknowingly and kept him in his bathroom overnight because it was cold outside. He and DH talk outside quite a bit.
I really DON'T like his houseguest/gf/whatever.. she barely talks, even when she did come pick up her kids, I opened the door and she said nothing to me, just looked inside to her child and said, "You ready to go?" She's just.. backward. I know that sounds bad but it's what it is.
So, if it were just her I'd have no problem telling her I am not interested in babysitting, ever. But I really don't want to alienate Neighbor, because we do value his friendship. I think for this instance I am going to go with the "we're really not comfortable with keeping them overnight" and if he keeps asking for other times, just say that the kids really don't play well together and it's too much to handle on our own.
I know that "it won't be possible" is the recommended answer but in a situation where I actually care about the relationship
I have with the other person, it seems pretty rude to me. I know that I'd be quite confused and probably cooling off the friendship if someone just told me they couldn't help me out, with no explanation at all.