Our children have 1098-e's and 1098t's. we cosigned on their student loans. Who's taxes do we file them under?

If they are dependents the forms should be included on your return. However if the 1098-T shows scholarship amount greater than education expenses the student might have taxable income on the difference. 

The 1098-E goes on the tax form of whomever paid the loan interest. You are both eligible, since you are a co-signer. 

The 1098-T is only an informational document. The numbers on it are not required to be entered onto your tax return. However receipt of a 1098-T frequently means you are either eligible for a tuition credit or possibly your student has taxable scholarship income. 

If you claim the tuition credit, because the student is your dependent, you do need to report that you got one on your return.

There are times when both the parent and the student, report the 1098-T, with adjustments. 

There's even a loop hole available for the parents to claim the credit, if the student is on scholarship.