Turn them off in the menu where you set up the game. That will help. It was designed to give the player options/issues aside from the main enemy. They are sort of a freelance mercenary force that you can pay off to attack someone else or just let them come and use them to rack up exp. points for your capital ships.

Unfortunately, Diplomacy pirates had their difficulty rebalanced so they would be credible threats to veteran players.  The problem is, a credible threat to a veteran player can be completely overpowering against a beginner.  Especially at the lower skill/difficulty levels, winning the pirate bid to subject your opponent to their raids is really all that's necessary to win, as a lower-difficulty AI and beginner players cannot withstand the powerful pirates of Diplomacy.  For this reason, I strongly recommend beginners turn off the feature.