Warning - newbie - just got PS3 a few days ago. "Send car to a friend is an option but is grey and can't be selected.
You should make sure you are not currently in the car you want to give away. Once you're in another car, hit the Profile link, find your friend, click the gift box icon, and you can select to give a Car, Item, Paint or Museum card. You should be able to give one car per day to your friend this way.