Most of the ink companies have a "Soft Hand" black available. It will be the same as the Chino/Softee/Fashion Soft bases. They just added black pigment to it.
The only one I remember is the Softee Black from QCM (gee I wonder why
). Ask your distributor what he has.
These Black inks are deep black and will be as soft as plastisol will ever get.
Other wise pick up one of the above bases to add to your black. You want the plastisol to penetrate into the towel like waterbase does.