Using Latisse As an Eye Drop to Darken Eye Color?

This is an inconsistent an unpredictable side effect of Latisse. Therefore it will not reliably change or darken the color of the iris. However, it does have a greater tendency to darken the eyelid skin

Please do not apply Latisse directly in your eye. It is only to be applied on the upper lash line to address eyelash growth, not eye colour.

Latisse is a topical product prescribed by a physician for lash growth. Actually, the "side effect" of the active ingredient, Bimatoprost, was the catalyst for the development of the product Latisse. Although the true purpose is to prolong the hair growth cycle for those who have insufficient lashes, it is being marketed as a cosmetic treatment to increase lash length and fullness for those who do not have eye disease or certain health issues.
To get to the original purpose of Bimatoprost (trade named Lumigan by Allergan) - this is a medication for glaucoma and the drops are instilled in the eye to control internal eye pressure.
You DO NOT want to take it upon yourself to use this product for the purpose of darkening your iris. Using the medication at that level without medical need could cause serious problems.
Latisse is used once a day in minuscule amounts on the surface of the skin next to the upper lash -- not in the eye!
If you want darker iris color, there are many safe colored contact lenses you can buy which will not jeopardize your eye health.

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.