The answer to your question is simple.....Don't shoot zoners......ever, at all. It's hard work getting back in thier good books. Goto Bethlahem station, try and take a zoner bribe or 3, this is assuming you can even get into the station. Failing that, make a new char.
Well actually killing BHG ships makes you friendlier with Zoners. Ive noticed that on Corsair char when killed dosens of em and realised that I have full zoner rep.
Wow! Thanks for this nice trick :D I have shot some Zoners accidently around the Ames Research station with my pirate character. I will try these solutions.
"It was the 23rd century, mankind's darkest hour. [...]"