This is another attachment for https://www.thingiverse.com/thing:3140367 The cone top does a great job, but the tip-down design leaves the dropper tips covered in paint.
I recommend printing the larger_bigger_coupler from the above link. When attaching this to the coupler, use epoxy and have the cup tilted toward the center axis of the coupler. Place the bottle firmly in the cup. The sides should be tall enough to hold the bottle, but do be careful.
I printed mine with the opening facing the print bed.