Is there a way I can get a deduction for paying off loans on which I was a cosigner?

No.     The only deduction you get for a student loan is for payment of interest on the loan.  There is no deduction for paying off the principal.

The answer to the poster's question is No. 

For others reading this, a related question is: Can I deduct student loan interest I paid on my child's education loan?

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

1. You actually 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