I cosigned student loans, son made no payments. I paid over 6,000. in interest last year [2019]. He is not a dependent. Can I claim interest?

Yes,  because you paid it and were legally required to (as co-signer).  There's one more requirement: he must have been your dependent at the time the loans paid for school.  He does not need to still be your dependent. 

The deduction is limited to $2500.

If you cosigned the loan and paid the interest you can probably claim it.  It is not necessary that you claim your son as a dependent.

 

You can claim the deduction if all of the following apply:

• You paid interest on a qualified student loan in tax year 2019;
• You're legally obligated to pay interest on a qualified student loan;
• Your filing status isn't married filing separately;
• Your MAGI is less than a specified amount which is set annually; and
• You or your spouse, if filing jointly, can't be claimed as dependents on someone else's return.

A qualified student loan is a loan you took out solely to pay qualified higher education expenses that were:

• For you, your spouse, or a person who was your dependent when you took out the loan.
• For education provided during an academic period for an eligible student.
• Paid or incurred within a reasonable period of time before or after you took out the loan.

See IRS Topic No. 456 Student Loan Interest Deduction