Suggestion: 1/7 wading area with a drainage hatch leading into the vomit-resevoir. Use pumps to push the vomit water around, and add a drainage hatch in the target area to allow re-use of vomit-water.
This way, your dwarfs vomit directly into the water to be drained, allowing easier resource control. Of course, This assumes you have a way to get the wading pool set up in a reliable, vomit inducing location. Do remember to regularly change and add water, as some of it will evaporate, and if you have too much vomit and not enough water, it's just thinner vomit.
I think there are a couple minor problems with this plan:
1) 1/7 water will evaporate quickly. Needs to be at least 2/7 (dwarves can still walk in 2/7 water, and it doesn't evaporate
unless weather conditions cause it to).
2) Don't pumps magically remove contaminants? If so, then the vomit will disappear when pumped.
I think building a long trough of 3/7 water with ramps for access, sunlight in the trough but not on the ramps, and one or more floodgates to release the water would probably work well. Vomit can be collected ahead of time and stored for "emergencies".
You'll need to fill it exactly to 3/7 on every tile, or it will slosh around and some of the vomit will likely be destroyed, bucket brigade is probably the best method.
I picked 3/7 because 2/7 won't flow very far or very fast, and dwarves can still stand in 3/7 water. 4/7 starts them swimming, but they can't drown in less than 7/7, so 4, 5, or 6 might be an option as well; assuming dwarves vomit while swimming with no ill effects, the level should be picked based on how much is most effective in delivering the payload to the target area.
≈≈science
≈≈ will be required.
One option for delivery would be to make one wall of the vomiteria floodgates adjoining the vomit-trap hallway so you can pull the lever and release a wave of vomit to fill the entire hallway with vomit quickly.
Placing the vomiteria above the target zone with a wall of floodgates opening to pour the vomit out the side of the vomiteria and down onto the goblins would probably work too.