The link below connects you to the Florida MLS whereby using the search for Sarasota County you will be able to view all MLS rental listings. Please contact the individual realtors who are listing the rental for further information. 

http://search.awp281504103.mfr.mlxchange.com/AWPResults.asp

However, using the search button to the left of this page gives you a far more detailed explanation of rental and vacation properties listed by Property Management companies and individual Landlords, some of which are not listed on the MLS.