AA sometimes has at least one Freethinker meeting in every city. No praying, and no god talk. Just talk about areas where the person is having a hard time, or ways that they have overcome tough issues.

Smart Recovery. I have several friends involved with it, totally non theistic. [smartrecovery.org]

Alcohol addiction is common, so avenues will be (somewhat) defined by your insurance or financial capability. To the extent that one shows willingness to pursue therapy, that therapy can include referral to clinics and/or treatments. Spravato clinics (ketamine) have become more accepted.

[cnn.com]

Psilocybin and other hallucinogens have shown efficacy in providing the rewiring needed to defeat addiction. Of course, use of hallucinogens can be hazardous, and decriminalization programs usually require an experienced guide.

Many universities currently conduct research programs in this process, so research in your state may be available. It's likely that a number of start-up pharmaceutical companies are conducting research using their own novel, patentable hallucinogens (tryptamines).

Some companies may be willing to ship microdose psilocybin to your location, however microdosing to alleviate alcoholism has little exploration. Or, travel to a therapy-friendly state. For certain, some people travel to visit Spravato clinics.

[i-d.vice.com]

CFI - Center for Inquiry used to have an associated agnostic support group for alcoholism.

[sossobriety.org]

This is what I found on Google.
[sossobriety.org]

SMART