First of all, its hard to have a rivalry with teams you don't play. Ole Myth and MisStake stomped us for years, but when we started beating them more often than not (we own the series against State and took 5 of the last 7 against Ole Miss), they took their ball and went home.
While we lack a "heated" rival like Louisville (last baseball game here with UofL ended in a brawl after we came back to win in the ninth) or TCU of the past, I would say Memphis. Its known as the Black and Blue game. While we own the series by a large margin, Memphis has picked up the wins lately, beating us twice at home. After one of those wins we found our bronze Eagle at the Rock painted Tiger Blue Sunday morning. They beat us last year at the Rock with a QB from Hattiesburg High, so the heat is picking up.
Some will say East Carolina, but IMO too much respect among the programs for it to become heated. But with ECU taking it to the next level as far as budget, fan support and fund raising, that may change. Others will say its the Battle for the Bell with Tulane, but for me, the series is too one sided and with them now being in the West, playing them only 2 of 4 years, the game has lost some luster. I'll throw in Houston too. Again while the series is lopsided in our favor, with a Championship on the line, the Coogs always get the best of us.