The following site shows an algorithm for computing the longest palindromic substring in O(n) time, and does so by computing the longest palindromic substring at every possible center and then taking the maximum. So, you should be able to easily modify it for your purposes.
http://www.akalin.cx/2007/11/28/finding-the-longest-palindromic-substring-in-linear-time/
EDIT: The first link looks a little shaky upon closer inspection, so here’s another one:
http://zhuhcheng.spaces.live.com/Blog/cns!DE38E96268C49F28!311.entry?wa=wsignin1.0&sa=707413829