There is actually only one pirate group in the game, regardless of whatever impression you might have. If you go to the Argo's bottom selectable, you'll be able to read your current score with all the main factions, including the pirate group. You won't need to ally with them in order to have/buy access to the Black Market, but the worse your reputation with them, the more expensive the items will be; IIRC, having a top negative (-100) reputation with the Pirate faction will inflate the cost of everything in the Black Market to +1000%.
Ultimately, it's all up to the player to juggle the reputations between the factions towards whatever main goals of said player are. Want to have the option to buy regularly in the BM? Then it might be a good idea to, for every Mission and/or Flashpoint you run against them, to counter with a handful or more for the Pirates. Note that the player can't ever improve or worsen the reputation with the local government of the Periphery systems, so you can always get your rep back up with the Pirates by going to a Periphery system and running Missions for the Pirates there; just make sure that said missions will be against the local government, as I can't remember right now if it's possible to take Missions for the Pirates against a main Faction in a Periphery system.
EDIT: Just to clarify, I know that the player can take missions for the local government against a main faction, i.e. Federated Suns or Magistracy, but I can't recall if all the Pirate missions available are always against the local government or if it can also target a main faction.