You asked for them, and now they're here... Star Trek Emojis from EmojiTap. And, even better, the app and one set of emojis is free, while other sets are just 99 cents per set. Among the 10 Star Trek: The Original Series images and phrases in the free set are: Kirk/All Hands to Battle Stations, Orion Slave Girl/Dance Like No One Has Danced Before, Rand/Where Yeoman Has Gone Before and Khan/Khan You Dig It.
The next set, at 99 cents, includes Scotty/Are Ye Daft?!, Sarek/Want to Mind Meld?, Andorian/Antennae Are Tingling, Sulu/I'll Protect You Fair Maiden; Dr. McCoy/Are You Out of Your Vulcan Mind, and the Gorn/What You Gorn Do?