While Liberia touts itself as an 'International Airport', it's really quite small so I'm guessing they just don't have the options that San Jose would have.
While I haven't had issues with liberia, I would recommend seeing if a travel agent can try and book the flights for you (like liberty travel where they'll check for free). I had similar issues when trying to do a multi destination trip in africa and it wouldn't work online even though the flights were there. Liberty was able to do it with no problem. This is assuming of course you can find individual flights from that airport but not connected.Edited: 10 January 2012, 15:02
It is not a direct flight. American has you flying to Miami first then back to Belize City. The poster did not say anything about a direct flight, just a flight to Belize from Liberia. I just did a flexible date search for the month of Feb. and came up with results each day. I chose BZE as my Belize airport code. I had to pull it up again just to make sure that I didn't mess something up. :)
Or -- use Taca which goes through Tegucigalpa.