I am going to split up the infield to the corner infield (1B,3B) and the middle infield(2B,SS). Any player who can play multiple positions will be listed at their primary position, but I will mention what other position they can play.
Richie Sexson- Sexson is not the same player he was when played for the Brewers, but he still has power ability and no major injuries recently. His numbers started to turn south in 2007 as his production went down. Although the Rays don't have space on the Major League for another first baseman, the Rays are weak in that position in the minors. Sexson is insurance if a Rays 1B/DH gets injured and he will be ready to come up. But the Rays shouldn't be too serious as a team in need of a backup first baseman with power.
John Lindsey- A right handed first baseman who has played 14 seasons in the minors, Lindsey(image below) had only reach the AAA level in 2007. He almost quit baseball after the 2006 season, but went to the LA Dodgers spring training and has his best two seasons in is pro career. He has improved his ability to hit and his plate discipline as he got older. Lindsey is becoming a AAAA player and the Rays could get him with an invite to spring training. If Lindsey has the same production this season as he did the past two seasons, I expect him to be in a major league uniform in 2009 or 2010.
Jason Bowers- Another journeyman, Bowers was brought up as an shortstop and has moved around and may switch to third or second as his primary position. Not a great fielder, he his an average hitter but has improved his plate discipline the past few seasons. Bowers has the ability to steal a base as well, 16 a career high in 2007. Bowers may be a better minor league utility player option to Elliot Johnson, who strikes out too much and is a worse fielder than Bowers. Just minor league filler at best who has to compete with Johnson for that spot.
Andrew Pinckney- Andrew Pinckney is a left-handed hitting third baseman who is still relatively young, 27 next season. A marginal prospect, Sox Prospects says he is a average fielder with a strong arm and is average hitter who can hit for power. Still needs time to develop some, but could compete for a spot at third or first for Durham if signed.
The best pick out of this group would be John Lindsey, who has the best potential to play in the big leagues and play well.