If it's a family member... it's probably a double no-no.
1.
Seriously though, what is says back in Proverbs about cosigning is that it's a snare for you financially.
Because there is a good chance you'll end up having to pay the debt.
If you are able to pay the debt, and wouldn't mind paying the debt for the person if needed,
then cosigning is fine.
2.
There is also a theory that many people hold, which goes like this:
if a bank won't give someone a loan, and they are "professional loaners",
then it is unlikely to be safe for YOU to give them a loan.
(Doesn't mean you shouldn't cosign for a family member...
just means you need to look at things in some different ways.)
3.
If they can't make their payments, and you have to pay the loan,
will that damage the relationship?
This is a very serious thing to think about.
Anyway...
like any major decision, I'd give it some serious prayer.
Tell them you have to think about it... then take some time, and really pray over it.