Yes, you can dye it black. I've done tack repair and made tack for about 12 yrs as a hobby. Black is a little more difficult to do. You may need to do more than one application. Black tends to bleed off when it gets wet.
Clean the leather. Apply Fiebings dye with a barely damp sponge, or cotton cloth, or use wool daubers. Apply a light even coat with a wiping motion. Let dry for 12 to 24 hours. The leather will feel dry in just a few hours, but I have found the added time lets the color set in.
Wipe the leather with a clean cloth, you'll probably have some of the color come off. Apply a second coat, and let dry. Apply another coat if necessary. Again, give it a day or two or three to really see how the color will set. I've dyed some projects that looked a lot different 4 or 5 days later.
If you're satisfied with the color, you will finally need to apply a sealer. Resolene works well, Leather Balm with Atom Wax works too, and will give a bit of shine to the leather. You can also ask the salesperson what they would recommend when you buy the dye.
You may end up with some dye on your fingers, it WILL wash off eventually. Some people use gloves, but I find them annoying.