Is your cousin trying to get a new loan? If not, she probably does not need to do anything except continue making payments on the mortgage ... if the mortgage is subject to the "Garn St. Germain Act" [12 USC section 1701J-3(d)(5)], the lender cannot call the loan if the loan was transferred to a relative as a result of the death of the borrower: so even if your cousin couldn't qualify for a loan on her own, she can continue to pay her father's loan and the bank cannot force her to refinance.
The information you obtain at this site is not, nor is it intended to be, legal advice. You should consult an attorney for individual advice regarding your own situation.
She has a lot of choices: as examples, she can have an investor on the loan or have it guaranteed by a third party if they're willing to do it. Maxwell Livingston practices in Albany. I'd suggest that you call him about structuring any transaction and loan and any estate work that you need.