Jim, there's no advertising or promotion of particular realtors on City Data - have you tried just contacting some of the nationwide realty companies? I would think Jacksonville would definitely have rental agencies since there's a turnover with the air base.
Have you tried the Democrat online? Craigslist might also have something, although it doesn't look like there's anything real new on there today.
Classifieds : Search results (L9__)
You can change the parameters to J'ville or Austin as well...good luck.