Soon as it says they are inbound put a carrier or 2 in the system and bulk up that regions defenses.
In which system? Generally, there are more than one they can attack -- on some maps, as many as 3 or 4!
exactly, in my first game yesterday they actually went past my ally's 12 gauss turrets and two hangars AND past an attacking enemy fleet (so the pirates jumped to my ally's planet) just to attack me and they also ignored my nicely defended arctic colony to go to my undefended homeworld. I completely missed that possibility so I got quite beating. against the ai they attack the same location all the time though.
so bottom line: like them, like their strengh and the way their arrival is announced and that you can deflect them. maybe have the pirates have some hate level towards players so that they don't always go for the one with highest bounty, cause that makes it a bit too predictable. also have them explore more diverse routes, so that they don't always attack the same place. that may be had as there aren't always routes avaible, but hey.
one the hate thing: yes, unfair if you are the one picked on for no particular reason, so maybe let factors influence it such as number of trade ships (pirates want to plunder after all), general wealth in ressources or general military strengh (hey, after all you are a menace to them and they should take that into account).
lastly, I may be too stupid, but for new players a quick destription of pirate ships functions would help, so you can better prioritise targets.
one more option: lets say you have a lot of money, its a free for all game and your fleet slots are all full. it could be interesting to give some money to the pirates and they start building a capship or some other strong ship (and are of course grateful and not attack you unless massive bounty is on your head at which point you wont do it anyways). not sure how realistic or useful it is, but ideas are ideas.