Hi Larry!
I have recently been answering several similar questions about the Woodturning Fundamentals answer about food safe finishes. I'll post a portion of that reply which interestingly was on the same topic about finishes useable with an alcoholic beverage:
The issue of what to finish turned vessels with if it is known they are to be used with wine, beer, mead, spirits, etc. comes up repeatedly over the years on various internet forums. Historically, either no finish was used (bare wood), or in some cases wax (e.g. beeswax) was used to line the vessels, and might have to be re-applied periodically. When making wine goblets, beer steins, mazers, etc. I would not advise using a shellac finish (it is too easily damaged or dissolved by alcohol solutions, potentially even with dilute ones). Using polyurethane has been successfully accomplished, as has the use of epoxy to line some drinking vessels (I know of other homebrewers who use epoxy-lined turned wooden beer mugs for drinking beer and mead at SCA festivals). Both of these surface reactive finishes will polymerize to a water- and alcohol-resistant "plastic" film, and should stand-up to most liquids which are meant to be consumed. The major challenge will be to assure that the normal wood movement with humidity (and to some extent temperature) does not create problems with stresses and cracking if a rigid "plastic" liner of applied poly or epoxy coats the inside of the vessel without a corresponding surface treatment on the outside of the vessel (remember the old woodworking adage to finish all sides of the piece similarly). Once the surface finish is polymerized and "done curing", before use I would be certain it was washed thoroughly to remove any unpolymerized epoxy resin or polyurethane. A surface wash with denatured alcohol, followed by a thorough cleaning with soap/detergent and water should prepare it adequately for beverage use.
If you elect to use "no finish", I suggest sticking to hard, dense woods like hard maple or beech, or perhaps even cherry or poplar. I have been told walnut vessels can impart a flavor into the beverage/food, and should be avoided. If no finish is used, expect the inside of the vessel to be stained from red wines, etc., thus adding some 'character' to the vessel.
In any vessel meant for drinking, I also would be careful with using exotics, especially woods known to be toxic, such as cocobolo. I could only imagine what kind of pain and suffering would ensue if the toxic chemicals (dalbergene and related chemicals) were dissolved in an alcoholic beverage and ingested. Alcoholic beverages would have an increased likelihood (compared to water) to dissolve extractive chemical compounds from the woods used, so caution is advised here.
I agree with Mark, that few finishes will stand up to repeated applications of very hot (boiling) water. However if you are preparing your coffee and/or tea correctly as an infusion, the water should be no hotter than 170^F, and you might experiment with epoxy or polyurethane finishes, although there is no guarantee that these finishes will stand-up to such heat. You might also try using no finish at all with woods such as hard maple or beech.
I hope this helps!
Good luck!
Rob