Usually you have to pre-arrange c&i facilities when submitting flight plans. Facilities are available in some but not all airports, and some of the airports that offer them need varying amounts of notice (I've been told anything from 4 hours to 3 working days).
Obviously, the flexibility of the authorities in the destination country is bound to increase if you're travelling on official state business.
I have never travelled on a private plane so the above info is through the experiences of friends who do, and as such may contain slight inaccuracies.