I'd only tag private inside parking as an [entrance][1]. Indeed there is a not entirely insignificant number of entrance=garage tags.
If you mean the parking is outside, I'd simply put an [access][2] tage on it (likely access=parking). access=private). Connected buildings can be either retraced as separate linked buildings, or as a single building=terrace, if you like that better.
[1]: http://wiki.openstreetmap.org/wiki/Key:entrance
[2]: http://wiki.openstreetmap.org/wiki/Key:access