Black is a color that you can do with either dye or paint.
For new saddles and leather
in general I think dye is the way to go, because it gets all through the leather and becomes part of it. Dye really is permanent. The problem is an oil dye is going to mix with the shoe polish and other waxes in the saddle, if there are any, and may never dry. If it doesn't dry, it will ruin a lot of pants. So in this case I'd go with paint.
That said, for the sake of "what if...", IF I were to use dye I would use Fiebings oil dye. It only takes a tiny bit of that stuff to turn leather permanently black. It is sold with a "resolene" acrylic finish that you put on soon after the dye and it seals the surface nicely. The combination, properly applied and burnished, is really nice. I wonder if the resolene would be all you need... but the bottle of dye is something like $8 and you only need a little of it; and the resolene is something like $8 IIRC and you would only need a little of it. I'm still thinking paint is the way to go.
A jar of Angelus leather paint costs about $3 and will paint several saddles. I have used the stuff two or three times; once on a customer's saddle (white) and once on my own (turquoise) and... the third time I'm not sure. Maybe I'm thinking of a saddle for @
USAZorro who can comment further.
Anyway, the place that sells you a $3 jar of Angelus leather paint will also sell you a $3 jar of Angelus deglazer, which they recommend using before the paint. With new leather I figure that stuff isn't necessary, but in this case, especially since kiwi shoe polish was mentioned, I'd definitely get the deglazer, and I might use something even stronger to make sure the leather is really clean, before painting. And let it dry thoroughly before and after painting, of course!
I'm sure there are other brands of leather paint, but the place I go to (Manhattan Wardrobe Supply) does a huge business (Broadway is a couple blocks away) and they sell Angelus paint. Good enough for me!