Well, we have a series and episode seed thread, in the Narrators room to help you come up with a story/plot. There's even a 'roleplaying an Abrahmsverse game' thread around here somewhere. And I have all kinds of crazy trek based ideas that I post here; feel free to steal from my brain (God knows Hollywood does).
Do your players want a JJ themed game, or are they going to accept that there is usually some thought in Star Trek? ("sure, you broke the rules and we were going to kick you out, but you stopped a bad guy after he killed a billion people, so have command of our finest ship instead")
I myself liked the NG era, but I did like Enterprise a lot.
Sadly, a new Trek show would almost HAVE to be connected to the Abrams universe. No studio exec would green light it without having the big budget movie tie in.
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"Yes, it's the Apocalypse alright. I always thought I'd have a hand in it"
Professor Farnsworth