We told everyone when we had our first, that everyone was welcome to visit, but that they would need to find a hotel or something to stay at. I think it is perfectly reasonable.

In our situation, what ended up happening was FIL came up for a couple of days - stayed in a local cheap boarding house; My parents came up for a week and stayed in a hotel, my sisters stayed at friends houses; and my MIL chose not to visit straight away (due to lack of funds) and visited us a couple of months later for 3 weeks. MIL grumbled a little when we told her we didn't want anyone staying, but couldn't really argue as none of the other parents were 'allowed' either.