If the loan will be sold to the secondary mortgage market, Fannie Mae and Freddie Mac have a $50k lending requirement. If you are looking to remodel the property, consider a FHA 203(k) or a HomePath loan which can wrap the two into one loan.
Another option is to look for a lender or credit union that will hold the loan in house. Or you can get a personal loan. Or you can get a HELOC off your personal home. Or you can borrow from your retirement account. Or you can buy on land contract. Or you can max out a credit card for a fix and flip deal.