I've only seen Sunslayer at Bruschal Base in the Frankfurt System.

Anyone know what the faction is there?

The faction that runs it is the Bundschuh.

Sigh...that's not gonna be good...you know off hand who I need to kill to get them friendly? Or better yet, where to bribe them?

Well, let's see. Their main enemies would be the Rheinland military/police, Outcasts, and Corsairs. There is a sticky thread that discusses where you can bribe ppl...but the only place I found to bribe them was from their own base (which kinda sucked hard). Although, once you land you could do a few missions for them and that should bring your rep w/ them up a bit (but be careful not to piss off the ppl you're flying against--typically the Rheinland military). If you want to stay on the right side of the law, just kill Outcasts like there's no tomorrow. Cheers.

Who cares about being on the right side of the law. It is much more fun having all the houses hate you and trying to use the tradelanes and jump gates. Other players just sit back and watch the light show I create

The best people to kill to get in with Bundschuh would be Daumann and Kruger, IIRC.