Don Best provides that info on their premium service. Try signing up for an island express free account and see if they do the same. All you have to do is click on the box that will eventually have the score when you see an L listed beside the game time on the left hand side.
Comes out lookin like so
Weather updated at 06/05/2003 15:33:42
TORONTO BLUE JAYS AT ST.LOUIS CARDINALS 8:10 PM EDT
----------------------------------------------------
MOSTLY FAIR, WIND IN FROM LEFT CENTER 5-10. GAME TEMP 75, RH 44%
===
TORONTO -
(06/04 05:51pm) OF Shannon Stewart (hamstring) has been placed on the 15 day DL.
TORONTO AT ST LOUIS -- LINEUPS
TORONTO ST LOUIS
AVG HR RBI AVG HR RBI
Reed Johnson RF .308 2 7 Miguel Cairo 2B .257 1 7
Frank Catalanotto LF .326 5 32 Jim Edmonds CF .290 12 33
Vernon Wells CF .289 12 55 Albert Pujols LF .369 15 43
Carlos Delgado 1B .327 17 58 Scott Rolen 3B .297 11 46
Tom Wilson C .315 3 16 Edgar Renteria SS .346 6 42
Orlando Hudson 2B .292 2 25 Eduardo Perez RF .315 3 9
Dave Berg 3B .300 3 13 Tino Martinez 1B .258 4 21
Chris Woodward SS .256 2 21 Mike Matheny C .281 2 22
Mark Hendrickson LHP .000 0 0 Woody Williams RHP .240 0 0
(4-4, 5.79) (7-1, 2.19)