Can I enter daughter's student loan payments?

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”)

Yes. 

According to the IRS 

Generally, you can claim the deduction if all of the following requirements are met.
• Your filing status is any filing status except married filing separately.
• No one else is claiming you as a dependent on their
tax return.
• You are legally obligated to pay interest on a qualified
student loan.
• You paid interest on a qualified student loan.
 

@ekggraphics