It depends on the type of property. If it's a "public accomodation" like a restaurant or hotel AND it is engaged in interstate commerce then no, you cannot discriminate. As an interesting side note: A small cafe in LA or MS wasn't serving blacks. The Federal Gov't got involved and a court ruled that since they were buying their ketchup packets (or something like that) from out of state, they were engaged in interstate commerce & the civil rights laws applied.
If you're talking about a truly private place like a home, then you can discriminate all day long.