This suggestion is not about being able to dye potions in a brewing stand or cauldron, please read before posting.
Currently, in order to choose a color for a custom potion, you have to pick from the preset colors of the potions that are already in the game. This is done by simply using the default potions damage value for the damage value of the custom potion. This gives you a limited palette of colors to choose from.
I propose that we be able to change the color of a potion using NBT editing programs by adding and/or editing the color tag in the display properties of the potion.
We can already do this with leather armor, allowing armor colors unobtainable by simply using dyes. Likewise, the potion color is already applied as a color mask to a base image, as can be seen here.
I can see this as a nice addition that would be very easy to code and implement, and could greatly expand the use of potions in adventure maps. Look HERE for more information about what I am talking about.
Sounds like this would be awesome for adventure maps. This could get a bit awkward in survival, where you could mistake a potion's effect later on because you made it a color similar to another potion, but simply hovering over them with your mouse solves the issue.