You might ask over at the paint forum as well as here, but tinting a primer close to the color you are going to finish with should help. You might need two primer coats follwed by the color coat which is opposite the standard paint schedule of one coat primer/two finish.

Some primers say on them for dark colors, and the primer itself is greyish.

Porter Paints has a primer called 'Blank-it'. Works pretty well to kill the dark colors. 2 coats of primer may be required. Of course, you can skip the primer and just use 3 coats of finish.

we painted over dark stained cabinets, painted them white after putting a couple coats of Bins primer on them.
Sierraeast is right about checking in the paint forum, have some good pro's over there.

Using a good quality paint will help. Walmart's paint is like water. I painted over very dark hot pink walls in my daughters room when she moved out using Behr paint from Home Depot. I painted over with one coat of baby blue and was floored when it covered it all. I didn't even use primer. I don't know if that helps, but good luck.