When I was just finishing college and NEEDED a reliable car for my first job, my grandmother told me she'd co-sign for me to get that first car loan. She made it clear that she'd do this for me ONLY ONCE. She explained that if I made the payments on time, I'd never need anyone to help me with getting a loan again. And if I failed to make the payments on time, she'd take my car and sell it, and she would not help me again financially. It was good advice. I did my part, and it was one of my first steps towards financial stability.
At that point I could have obtained a loan on my own, but it would've been at a higher interest rate, and I made so little money that the difference was significant to me. I very much appreciated her help. It was a vote of confidence in me.
I will do the same thing for each of my daughters. ONCE.
They've been reliable in other ways, and they've done nothing to make me think they wouldn't pay their bills, so I'm willing to help them get a good start.
I would do a couple things to protect both them and myself:
1. If I'm co-signing, I do have some say-so in what they buy -- I'm assuming we're talking about a first car, aren't we? I'd insist they choose something moderately priced, perhaps a Toyota Corolla or a Nisson Sentra. If they are unwilling/unable to make the payments for some reason, I can pay for a car in that price range without any difficulty, and -- like my grandmother -- I'd be perfectly willing to take the car and sell it, if things went badly. I'm not going to find myself in financial distress over a moderately priced car.
2. I would also insist that they not buy a new car until they had a couple months of payments in savings; thus, if they find themselves without a job suddenly, they wouldn't be unable to make their payments. I've always taught them never to live too closely to the financial edge, so this would not be a shock to them.
3. I'd be sure they had comprehensive insurance so that if the car were wrecked, they wouldn't "lose everything" they had in the car.