There's an app called MLB Clubhouse (search for it in the iOS App Store) that has a smattering of Dodger Emoji. You can check out the ones based on specific players below.
This first one is pretty obvious, if not exactly a great emoji: playoff hero Clayton Kershaw, who won on 3 days rest tonight in Game 4 of the NLDS.
Next we have Zach Grienke. The emoji actually captures his dead-eye stare pretty well.
Justin Turner is the best candidate for an emoji and this one delivers.
Yasiel Puig, who returned from the DL and has played in one game in the playoffs so far.
Guessing this is rookie Joc Pederson? Or maybe SS Corey Seager? Could be a young Chase Utley for all you slide fans.
Adrian Gonzales, the "butter and egg man" according to Vin Scully, and the team's most consistent player.
Go Dodgers! Diamond Vision 4 life!