Get a big mixing bowl and put one cup cold water and a tablespoon of vinegar in it and stir. Dip a clean lint-free towel or cloth in the bowl and start blotting lightly from the outside of the stain in. Repeat using clean areas of the towel each time until you have removed all all of the stain. Lay another clean towel over it for awhile, but don't push down, and that will wick all of the moisture out of the felt and into the towel. Check when dry and hit any spots that didn't go away 100%.
Don't rub the felt when you are cleaning or drying, because it will stretch and then you will be S.O.L. and your dad might use one of the pool cues as a sort of do-it-yourself prostate examination.
Not speaking from any kind of stain removal from a pool table felt viewpoint but if all else fails, in hopes to avoid the costly replacement of said felt you can try resolve carpet cleaner. It does wonders. My father used to re-felt the tables at the gentleman's club he belonged too and the proper procedure cost $200, and that was 30 years ago. It's also something you shouldn't try yourself, as the felt must be applied and stretched at exact specs and tensions. Then again it depends on the table. A $600 table from Sears is one thing. A $5000 1" thick pure slate is another.