The link below contains a roster of the 1st (Watie's) and 2nd (Adair's) Cherokee Mounted Volunteers, plus Holt's Squadron.
It is an index of name and rank only, based on the National Archives compiled service records, but arranged by COMPANY, with separate listings for the first (July 1861) and second (July 1862) organization. Thus, it is a much more accurate list than the one found at NPS Civil War Soldiers and Sailors System, which does not distinguish between the first and second "edition" of Watie's regiment, with two entirely different company structures.
There are a few errors on this roster too, however. Some officers and men are listed two times in different companies of the 2nd (Adair's) regiment. This is because Adair's regiment was formed from Bryan's 1st Cherokee Partisan Ranger Battalion, resulting in changed company designations (e.g. Company A of Bryan's battalion became Co. D of Adair's regiment).
The roster may be downloaded as a .zip file, and comprises 32 pages.

http://www.quillspirit.com/History/Civil_War_Data/Waties_Regiments/