If you have the Diplomacy expansion, with appropriate research, you can issue your own missions to AI players, and eventually, the Pirates as well.

If not, well, the only thing close to issuing a mission is to Ping your ally. To do this, select any of their ships, and if you have a Cease Fire (or Peace Treaty) you will see three options on the bottom right - one is an attack request, another is a defense request, and the last cancels your last request. When you click, you will be able to select a target planet to ask your ally to attack or defend. There is also a "general" ping (denoted by an icon of yellow concentric circles) where your allies will try to guess as to what you want them to do with that planet.

Keep in mind that AIs don't always want to comply with your requests. The better your relationship with them, the more likely they are to follow up on your requests.

Ah, thanks. I was looking for a button like that. I'll take another look.

...I actually tried doing the attack/defend planet command thing, the AI says something like "alright" or "Roger that"...and their ships just sit there the whole time...

I never get a reaction from them, I just stopped trying.

-Twilight Storm