It is far better to count or sing objects that aren't human beings. You could count toys that are occupations (police, fire fighters, etc.) or animals, or, familiar objects. Below is some of what I found in the image search I did.
The "Indians" on one website are white. Completely white. As white as the Pillsbury Dough Boy. They're about 6 inches tall and their teepee is 20 or so inches high. They have a canoe and a fire. On another site, they're bright orange. On some they are brown. Precious Moments offers ten little "Indians" and a teepee, and, an entire family. Stereotypes abound, from names to clothing the dolls wear. Sadly, there's a lot of teacher resource sites that include worksheets using the poem.
The history of the rhyme/poem/song is important. See "Commentary: Ten Little N***** Girls" at the Essence website. Do read the commentary.
A Teacher Reconsiders Ten Little Indians
INDIAN BUNNY. No! Now it is BRAVE BUNNY --- And TEN LITTLE RABBITS
Instead of Virginia Grossman's TEN LITTLE RABBITS, read Michael Kusugak's MY ARCTIC 1, 2, 3