As per this FlyerTalk thread, Aeromexico is offering LAX-MEX-SJO round-trip in Clase Premier for $566.67. Economy fares to SJO run about the same price. This fare earns 6890 miles (8.2 cents per mile) with the business class bonus. I was able to find several dates in June, July and August though prices jumped in September. I didn't look beyond that.
Sample amazing coffee, zipline through cloud forest canopies, and explore nearby volcanoes. August is also a great time to take a day trip to see the turtles hatching in Tortuguero. This is a great opportunity to experience Costa Rica's "Pura Vida" lifestyle.
(HT to Bacai)