Generally, no. You have gotten your own financial house in order, and should not risk that stability by placing it in the hands of another.
When you co-sign or guarantee the debt of someone else, you are subjecting yourself to the risk that they cannot or will not pay that debt. The creditor will then have recourse against you.
Just this week I dealt with a situation in which a mother had co-signed approximately $180,000 for loans for her son. The son is now finding it difficult to service those debts. His options are limited, at least if he wants to protect his mother.
While bankruptcy could discharge all of the debt for the son, the mother would remain obligated. The same is true with any negotiated settlements to reduce the debt, unless those settlements include the mother’s liability. And it will be far more difficult to reach settlements when there are two people liable rather than only one.
It may be possible to fashion the obligation with your child so that you are fully protected. Doing so will require some form of collateral or other assurance of ultimate payment.
There are also payment measures which can be put into effect to reduce the likelihood of a default by your child. Automatic payroll deductions or automatic payments from an account can help reduce the likelihood of default. They cannot eliminate that risk, however. An automatic payroll deduction does not work very well if your child losses the job. An automatic payment from a bank account becomes useless if the child changes banks or the account is empty.
There are lots of reasons why people, particularly parents, co-sign or guarantee debts for their children. Often those reasons are not very good.