Deer antler is not like horn. It doesn't burn well at all. It behaves more like bone than horn. I would suggest treating it like ivory, and scratch your design into the polished surface, and then ink it with india ink, or watered down artists acrylic paint. After inking the design, buff off the excess, leaving the ink in the etched lines.
Hungry Horse
+1
No small amount of heat is needed to get antler to burn. To get a permanent 'color' change, it takes approximately the same amount of 'focused' heat that you'd need to braze a joint, or ~840 F.
I finished the crown of my antler handled knife by burning it.
a.) First heavily soaked the crown in Neatsfoot oil, which I used not so much as a heat transfer medium, but as a temperature 'telltale' indicator.
b.) Using a propane torch, the antler crown was burned totally black (really heavily charred) until the oil boiled/bubbled (really bubbled, until almost completely burned away.)
c.) Then the crown was re-soaked, heavily, in Neatsfoot oil, for cooling and
d.) The charring was cut-back/burnished with plumbers 120 grit emery cloth, followed by steel wool.
Finished finish color looked like a cowhide saddle and varied, in color, across the face of the crown, lighter around the edges, where the heat dissipated quickly.
It took a tremendous amount of heat to ultimately attain a 'medium' depth of color. It came out looking pretty neat, but I was really fortunate that I didn't destroy it by getting stress cracking (antler was 20 years old.)
Antler is really tough stuff...
Good luck!!