In a few weeks, I have a flight arriving in to San Jose airport (SJO, Alajuela) very late at night (a little after 1am).
Can I expect to still find taxis there at that time of night?
However, TaxiAeropuerto (the bright orange taxis) offer 24/7 taxi service from the airport. I apologise if you can't read Spanish, mine isn't so great, but a rough translation of the last two sentences on that page is all you need:
Likewise, we transfer to the airport. We offer 24 hours service, 7 days a week
I imagine calling them to reserve might be a way to guarantee a pickup, but otherwise yeah, it sounds like you'll have no problem there.