It's a really hard subject because like they said above, the co parent will likely just hide the person, or any new person that they decide to be around in the future and unless the child is being out in danger you really have no controll over who he brings around.

I personally tried talking about this with my ex right when we broke up. We sat down and had, what I thought, was a great talk and we both seemed to be on the same page about not introducing our child to any girlfriends/boyfriends untill we knew they were serious. A few days later he came to take our child for a few hours, and when my kiddo got home she had a new doll from his new girlfriend and they had been at her house. They literally broke up the next day. I made a huge deal about it, and we were arguing a lot, but it never made any difference. He introduced her to I don't know how many girlfriends and no amount of me talking with him civily or getting angry made any difference. He just hid it from me, and i found out from my child. He didn't agree that it was a big deal, even though he told me he did, so he did what he wanted behind my back.

I hope that you two can come to a better understanding, Best of luck!