They are always fun. Kids love them soft toys and girls adore them. If you are a grown man and collect those, you might feel less masculine.
My professor used to buy them anytime he saw those at any thrift stores. He would put cramp on its head to flatten and dipped in water. So those stuffed animal would have thin head like smashed cartoon character with normal body when it is dry. Why did he do it? you are gonna have to ask him.
Anyway, there is a company called Rocket Craft that makes stuffed engines, cars and motorcycles in Sapporo, Japan. Where also nice beer is brewed. They mostly take commissions to make your car or bikes, but needless to say, it will cost you a chunk of change. Engine from 50 bucks to 300 bucks, car is starting from 350 to 400 bucks. If you want special tag plate on it, it will cost 40 bucks extra. Motorbikes start from 500 bucks to whatever depending on how complicated it is make. Those prices doesn't include shipping and hiring a translator. Both car and motorbike will be about 15-16 inches long. They also make trains, 3 wheelers, and whatever they think they can make. Stuffed Honda generator will be a nice pillow...
If you really want them to make your own, I suggest emailing them with Japanese or easy to understand English first. They will of course need the pictures of your car or bike to get you a quote.