If you choose to co-sign for your child's credit card make sure to explain to your child that the statements will get mailed to him and he must make payments by the due date. Explain that by making payments on time it is an easy way to boost and maintain a good credit score.
Opening a joint account with your young adult is another option. Since the statements will come directly to you, you won't have to worry about them paying the bill on time. If you have good credit, your child will benefit by sharing your credit history, which will boost their credit score. But since your child won't be paying the bills, they won't learn how to manage the credit card.
The third option is to add your child as an authorized user to your credit card. It is different from a joint account because the bank will think you control the card and not your child. But keep in mind authorized card holders don't benefit quite as much from sharing your credit history as a joint user would.