Using Latisse As an Eye Drop to Darken Eye Color?

I am not sure WHY you would want to do that. Eye color is a wonderful source of individuality and reducing them to black makes it a tad boring and ordinary.
BUT if you insisted on doing this crazy thing, you may consider having your PCP prescribe for you LUMIGAN, the glaucoma (eyeball pressure reducing) medication which WAS meant to be used as eye drops and is associated with darkening of the eye. Latisse is the same compound packaged differently in a small concentration for the cosmetic market.

This, at first blush, sounds like a clever idea. However, I can foresee four difficulties with this approach.
By placing Latisse into the eye itself you might cause darkening of the skin surrounding the eye. Also, results can be tricky. Your iris might become darker than you would like. This would be a difficult drug for you to titrate its effect.
Unlike the change to the surrounding skin which is reversible, Latisse into the iris would act much like a tattoo. The results are permanent. What if you or a loved one does not like the new color? You would be stuck with it.
Finally, by using Latilsse in this manner you would be transforming the ingredient from essentially a cosmetic tool into a medication. This would mean that you would be using Latisse, more like its identical twin Lumigan, including visits to an ophthalmologist to have your IOP (intra-ocular) pressure checked.
Investing in tinted contact lenses would be a better alternative.