Paint, in and of itself will not work. The results cannot be guarenteed, because of a number of variables, but you could use a fabric dye such as "RIT", and carefully brush it onto the cone with a foam brush- taking care not to saturate the paper excessively. The speaker should also be flt on it's back while you do this, and take care not to let any solution dribble down to the center.
Getting the color even is goin to be a problem.
If this is a vintage speaker, or highly desirable collector radio- I would leave it alone. It may have been made white for a reason, or it may have faded to that color, and the cone would be very fragile.
Regardless of vintage, you can always put some black silk of a very open weave, such as they use for silkscreening (although that is usually a white fabric), or some other open weave fabric that is black that you can adhear to a piece of foam core, art boart, masonite, etc, and place in front of the speaker, but behind the grill. This would work with just about anything but a long throw guitar speaker.
:i dont know anything about speakers and i've got white speaker cones, can i paint them or would it completely desroy them?