If you want to remove a cosigner from your loan, all you need to do is request a cosigner release form from the credit union. Schedule a meeting with a personal banker, sign the paperwork, and you’re done. (Note that this is not the same process if he’s a co-borrower.)
Just remember that the lender has final say in whether your dad can be taken off the loan. If you still have poor credit or limited income, the lender may not be willing to remove your cosigner. Make sure that you have the right mix of credit and income to justify your dad’s removal.