Usually, the bottom limit on a conventional loan is $50,000, though it depends on the lender. And I imagine that if you have a really good relationship with a local bank, you'd be able to persuade them to provide a loan for less.
However, just because you can't get a traditional loan doesn't mean that the property has to be paid for in cash. Or at least not your cash.
As Mott says, a HELOC or other line of credit will work just fine. I've heard of people getting loans for other purposes (such as a vacation), and then using it for something else. Just be sure you're not deceiving the lender.
Depending on who owns the property, you can also attempt to get owner financing. Let the owner act as the bank. You figure out the payments and length of time, or payments and interest rate, or any other variation, run it through a calculator, and you just do the paperwork with the seller and make your payments directly to him/her.
If you're short on cash and there's a profit potential, find an investor to contribute part or all of the purchase price in return for a share of the profits.
Hope that helps.