Black is tricky to make using oxides - easier with stains.
I do not use a black slip, but if I were going to make one I might
start with 1 part cobalt oxide (a strong blue colorant) with 9 parts
red iron oxide (a less powerful brown colorant) and 20 parts clay to
make it stick to wet pots (this is not for bisque). If you want it
to look black when you are using it, just add india ink or black
tempera. These burn out entirely during firing.
If it is not dark enough after firing, use less clay (some clay is
needed for adhesion).
If it is too blue, add iron or subtract cobalt.
If it is too brown, add cobalt or subtract iron.
You will note that these colors are opposites on the a color wheel -
so it is a matter of neutralizing opposites to get black.
If you put glaze over this type of black slip, it may turn blue (this
is the tricky part).
I have a good black glaze that is simply a medium dark brown glaze
with 6 percent cobalt added to make it black. When I overlap or
dilute it with another glaze, it turns blue. I use it for a night
sky background for my dream pieces.
One part black nickel oxide with two parts clay might might also work
for black slip but probably just grey. It may turn a bit green, so
some red iron oxide might kill the green. This black could be
combined with the cobalt and iron black to make slip that is less
likely to deviate under glazes.
Using a color inclusion stain (like Mason stain), one should be able
to mix black stain with just enough clay to make it stick to the wet
pots. Probably 1 part black stain and 2 parts clay. Stains cost
more because they are oxides that have been prefired with silicates
and then ground back to a powder for our use. This stabilizes the
color so it does not change much when we fire it. What you see is
what you get.
All this is simply off the top of my head educated guesswork based on
many years of working with the stuff. Please tell me what happens if
you try it.