Discharge white would work best on a black ribbed garment, assuming the garment is discharge-friendly and you're proficient at water based inks.

If that is not an option, print plastisol. In order to avoid a chunky (super thick/ heavy) print,  adjust your inks to print well on the ribbed fabric. We add curable reducer and/or soft hand additive when printing plastisol on ribbed garments to allow the inks to fall into the "valleys" of the rib.

You can cake on white plastisol and make it pure white, but the print may be too thick, especially on a tank top. With the thinned down ink, you may not get a 100 percent white print but, with the reducer and soft-hand additive, the ink with thin enough to drop into the valleys of the ribbed material which will allow for full coverage on fabric.  

When the plastisol ink is not treated with the reducers, it tends to do one of two things (besides being a thick heavy print): Either the print area will hold its shape and the garment will distort around it if stretched, or the plastisol print will split when pulled apart where it bridges (rather than fills, as it should) those valleys of the ribs.

This is why I say discharge is best.  Because printing discharge drives the ink into the fabric, covering the peaks and valleys of the ribbed garments evenly, and since there is no layer of plastisol ink on top of the fabric trying to bridge the peaks and valleys, there is no ink to split apart when stretched and the print stretches with the fabric. You do not have to worry about printing a thick layer of plastisol ink on top of the fabric to bridge those valleys, nor do you have to use any reducers or worry about splitting. 

The most important part of the process, however, is having a very open and honest dialogue with the customer.  Make sure they know that printing on ribbed is tough, and that opacity may have to be sacrificed for a soft print. I always suggest printing on a standard jersey material tank top for best quality; show the customer examples of each and let them make the decision.

--Dan Holzer, Forward Printing