What the others could have at least pointed out to you is that the green tickets have the same gift restriction that the cars themselves do. If a car can't be gifted due to the 1 million credit limit then the same goes for the car in green ticket form. What the others could also have mentioned to help you out was to tell you that you can trade level tickets or birthday tickets without any restrictions. GTPlanet (being the great resource for all us GT fans) has a list of what cars come from what tickets at this link:
The trick is in order to make sure you get the car you want you need to back up your save file to an external memory device like a USB thumbdrive before using the ticket. This way if you don't get what you want the first time you can exit the game and reload the save file that still has the ticket on it and try again. Sometimes you get lucky and get what you want in a few tries. But other times it can take 20 to 30 tries to get just the right car. It all comes down to how badly you really want that vehicle.
One last tip: some vehicles can be acquired through more then one ticket. Find the one that has the lowest amount of cars listed under it to help improve your chance of getting the one you want.
