I wrote a quick little script and let it go for ~36 hours to find out that these are the only alpha-numeric two-letter domains available in the .com .net .org suffixes according to the Internic Whois Directory:

However, most registrars won’t let you register two-letter .org domains anymore to comply with a new ICANN/PIR restriction.

There are no alpha-only three letter domains available. Zqx.net? Taken. Ywj.org? Gone. But there are 3777 .com, 22,176 .org and 16,562 .net alpha-numeric combinations still waiting to be snatched up.