The financing for this type of purchase typically works the same way as a home purchase. However there are many lenders who do not lend below a certain amount (often around 32K or so). Even those who will originate loans for parking spaces (which I'd assume are priced between 10-50K downtown), will often have to charge substantial fees to you (so that the originating lender does not have to pay for the loan itself- too complicated for a non mortgage professional like me to explain). Many times the amount of fees throws these type of loans into a high cost loan category which are more heavily regulated by the state, so many local lenders avoid them.
Just this weekend I asked three of my best loan people about doing exactly this and only one was able to do it. The other two's company's had effective lending floors of 100K and 150K. So it is possible, but I'd suggest pursuing financing via local (read smaller) banks and/or local credit unions and the like. They are more likely to have lending guidelines that allow for this size and type of loan.
Good luck and let me know if you need any referrals for lenders.
Broker Associate, Sudler Sotheby's International Realty
773-418-0640 (cell) 773-293-1200 (off) 312-577-0985 (fax)