Hi Shelly,
Since your boyfriend will not stop playing favorites, it may be best for your own child if you move on.
I know it hurts to think about, but you have to put your child first in your life. You really don't want her to grow up feeling like she is always going to be second to the son, and she is going to eventually start resenting him and your boyfriend, and even you, especially you, since you are allowing it to happen.
Kids don't understand the idea that you have 'talked and argued' about it with him, and he is still doing it. Kids see only the end result, that it is happening, and they will look to their parent(s) to stop it from happening. If parent(s) do not stop it, then why should the child trust the parent for anything?
This may seem extreme, but children really do feel insecure a lot, anyway, but in this type of situation, it can only get worse for her if it continues.
As for the boyfriend, I realize that he thinks he is helping his child, but he is confusing him more than anything. He is trying to buy his child's love by showering him with attention (and probably gifts) in order for the child to love him more than his mother. Sure, he can disguise this by saying that the child doesn't get that much love from his mother, but how in the world would he know that? His mind is probably still clouded with resentment over the breakup or divorce, and he is holding a grudge against the ex, so he can't get past the hurt and disappointment.
He needs to first get over the fact that his ex has joint custody, then he needs to talk to her about what they both expect in the way of parenting skills, and the main thing the child needs is consistency! If he gets treated like a king while living with Dad, he is going to eventually use that against Mom, even though she is probably doing everything she can to show him love without spoiling him. Dad's often think that they can buy a child's love, instead of being a normal father. When he was living full time with the child, he probably didn't act this way at all.
He needs to take a good hard look at what he is doing, and the signals he is giving his child, and you. If he can't get past it, you really may have to move on, for your own child's sake.
Good luck to you, and take care.