Molecular sieves / zeolites
AFAIK, JBH is right; there are no alcohol containing rocks in nature. Jed Clampett can't shoot 3 raccoon lengths to the left and become a beer baron.
This answer won't give you a great alcohol rock, but it can work with a little effort.
There are minerals that will adsorb small amounts of alcohol and hold it strongly enough that it is not readily eaten by bacteria.
They are zeolites and/or synthetic molecular sieves.
You either need to dehydrate natural zeolite at 170 degrees celsius and then soak the alcohol in, or make the synthetic zeolites and do the same thing. Synthetics have to be manufactured in autoclaves using organic templating agents, but they hold a lot more booze.
If they have the opportunity to hold water instead, they will take it, so getting them dry is necessary.
To release the alcohol, heat the zeolites at just above alcohol boiling temperature and capture the gas, or slowly seep water through it, displacing the ethanol as water adheres to the binding sites.
Other inorganic sorbents like activated carbon or special clays might work, but probably not as well.
You can react alcohol with sodium hydroxide to make sodium ethoxide. It's a white solid that's effectively 70% alcohol by weight. It's what used to be on those little refreshing KFC napkins many years ago (in my country anyway).
Add the correct amount of an acid (e.g. citric acid) and you will get an alcohol solution, potentially even a strong one.