As a co-borrower on my childs student loan, how can I claim the interest I've been paying?

You can claim the interest deduction, if you meet the three requirements:

1. You paid the interest
2. You are legally obligated to pay it (co-signing counts)
3. The student was your dependent, at the time the loan was used to pay for qualified educational expenses (the TT pop up says “when you took out the loan”)

In TurboTax, enter the 1098-E as if it was your own.