A quick Internet search of "Costa Rica Mortgage Loans" turned up a couple of brokers and private equity offerings.
You could also try to get the seller to finance part of the purchase price.
Or borrow it from your 401K, if you have one.
Depending on your credit score, it might also be worth looking at rates from a local credit union, bank, or even Prosper or Lending Club for a personal loan rather than a real-estate secured loan. The rates are usually higher, unless you secure it with a CD or stock portfolio or something. Both Prosper and Lending Club offer loans big enough to cover your 50% down payment.
Something I would never recommend to most people, but as a last resort -- if you absolutely knew you COULD pay it off any time you wanted, you could put the down payment or at least a big chunk of it on a credit card and float it between 0% balance transfer offers until you get it paid off. Discover, for instance, will deposit the money for your "balance transfer" directly into your checking account, and often has specials for 0% financing for 12 months with 3% up front transfer fee, or 5% financing for 18 months with 0% transfer fee. Chase Slate also has good sign up offers for balance transfers. Again, this is risky, and maxing a card will ding your FICO until you pay it down, and also increase your DTI -- if those things are considerations for your next home purchase. And if something happened that kept you from paying it off, your interest rate would shoot sky high. It's too risky for most people.