The answer to the Dodgers SI trivia question is Kevin Brown (March 29, 1999), who is the most recent Dodger featured on an SI cover prior to Manny Ramirez in 2008. We went almost 10 years without a cover, after being featured with frequency in the 1980s and 1990s. (If someone has a different answer, please let me know; the SI.com "SI vault" search system is extremely wonky, as one can access different sets of covers for "Los Angeles Dodgers" and "Major League Baseball Dodgers"--and neither of these cover sets includes the Darryl Strawberry "L.A. Story" cover from March 4, 1991 (which, come to think of it, may not be an accident).)
Now hurry up and start this Dodgers/Phillies game! I'm running out of things to fill the time, and I obviously don't want to work.