Distance 186km.
Allow 2 hours driving depending on time of day/week.
The airport is the other side of Seville from the Autovia for Huelva, Ayamonte, Algarve, Tavira.
There is a ring road that skirts Seville to the South that takes of right from the Airport - Seville road by the IBIS Hotel.However, it has a restricted speed limit. You need to therefore allow between 25 and 45 minutes to clear Seville and get onto the road South. From there allow 75 - 90 minutes to Tavira.
If you can pick and drop off the car at Seville Airport, this is by far the best option.
The only other option is long distance coach.
However, it is a hassle getting from Seville Airport to Plaza das Armas bus station. It is either a taxi or a bus to Stª Justa station and then another bus to Plaza das Armas.
See this post on my blog for info:
http://barlaventostravelblog.blogspot.com/2007/06/algarvefaro-to-huelvasevilla-summer.html
Also Have a look at this site which may assist:
http://www.solpraiaferias.com/index.php?content=cheg_en