Chris Brown -- Do Me a Solid, Judge ... Make My Baby Mama Shut Up!

Chris Brown wants the courts to do his dirty work -- as in, force baby mama Nia Guzman to quit bad mouthing him and talking about his fathering skills, or lack thereof, in public.

Chris and Nia are heading into court Friday morning to start hammering out a formal custody agreement for Royalty, but sources connected to the case tell us job 1 will be a gag order. Brown filed docs for an injunction blocking Guzman from bashing him to news media AND on social media.

Royalty's mom and dad have had very public beefs -- most recently when each accused the other of putting Royalty in dangerous situations. Sources close to Guzman say she thinks the gag order is a joke, since she only blasts Chris when he starts with her.

Also on the table today -- custody time (he wants 50/50), and monthly child support (she wants $15k/month instead of $2,500/month). This case won't be quick and easy. As one source put it, "It's gonna get nasty."

We'll be at court when the fireworks begin. Stay tuned ...

6:45 AM PT -- Nia just showed up at the courthouse in Houston. No sign of Chris yet.