I'm cosigner on a college loan with my son, but he just got married last year and I can't claim him as a dependent. Can I still claim the tuition from the 1098-T?

[Carl]

Generally, no. That's because in order to claim education expenses, he would have to be listed as a dependent on your tax return. However, if your son files his own tax return as Married Filing Separate, and he does NOT take his self-exemption, then you can claim him as your dependent and claim the education expenses.
Another thing too that's important. If your college student is the primary borrower on the loan, then depending on the amount of the loan you may not qualify to claim him as a dependent at all, regardless of his marital status. Hopefully, you the parent are the primary borrower. If the latter is true, then no need for me to go into detail.

[Opus 17]

For tuition, you can't claim tax credits for tuition unless you claim the child as a dependent.  And you can't claim him as a dependent if he files a joint return with his spouse, regardless of any other conditions.

If you have a loan that was taken out while he was previously a dependent, you can continue to deduct the student loan interest on that loan even when the student is no longer a dependent.  You must be a borrower or co-borrower (not a co-signer, that's different) and you must be the person who pays the interest.  If the loan is only in your child's name but you make the payments, the child can take the student loan interest deduction on their tax return because they treat the payment as if it was a gift from you to them which they used to pay the loan.

[Carl]

Key word I want to point out in Opus 17's correct response, is "joint return". If he files MFS (meaning his spouse must file her own MFS return if she has reportable income of her own), and does *not* take the self-exemption, then (and only then) can you claim him as a dependent and also claim all the education credits. My response has nothing to do with the 1098-E student loan interest. So hopefully you're not confused.