UPDATE - 20 January 2017
A Bernie Williams postcard has surfaced featuring Bernie at the bat, wearing a jersey featuring the "7" on the sleeve, memorializing Mickey Mantle who had died in August 1995. That means the "1993" list is probably a mix of postcards from 1993, 1994 and 1995 (or even 1996 given how the #7 was only used late in the season). Thanks to eagle-eyed Kid4hof03 on FreedomCardboard who pointed this out.
UPDATE - 31 December 2015
Thanks to Michael over at New York Yankees baseball cards, we now have solid information for splitting these postcards into individual 1992 & 1993 sets. The list below has been updated accordingly.
UPDATE - 25 June 2015
I'm now thinking this is actually two or three separate sets, or the set was issued continuously over two or three years. This morning on eBay I caught an auction with previously unseen cards of Danny Tartabull in a portrait shot, another Kevin Maas with a different photo and a Roberto Kelly. Kelly wasn't even on my radar for some reason, even though he was an All-Star for the Yankees in 1992, so I don't know why I was surprised. Checking the same seller's completed auctions turned up another lot that included Buck Showalter, Mark Conner and new-to-me cards of Clete Boyer and Yankee Stadium.
UPDATE - 15 January 2013
I saw the Maas postcard on eBay, so the set is now up to 26. I'm going to start posting images of each postcard as I find them so collectors might have a slightly better chance of recognizing them. I suspect the black & white cards are copies of the originals, but until I find color versions, these are all I have to work with.
UPDATE - 09 December 2011
A couple more of these showed up on eBay recently, but they are no help in narrowing the set down to a single year as all six individuals were with the team from 1992-93.
UPDATE - 04 December 2012
A much larger assortment of these has hit eBay, bring the checklist up to 25. I finally have verification of most of the starters of the team.
Here are the front and back together:
No joy on Googling SPORTSPRINT/ATLANTA aside from more references to that 1994 Greenville Braves set. Ditto for the photographers and what was presumably the outfit that provided the photos.