I hate to be rude, but I don't want a friend to stay overnight with me
Do you have something planned with them at your house?
I want to hang out with my friend at his house
Ask your friend to hang out at their home instead. I don't see any issue with trying to come up with alternate plans.
They just really want to spend the night with me, but I don't really have space for that.
If you don't think having an overnight guest would work out for you, just tell them that. I'm sure they'll understand.