What is the origin of the drug name Amiodarone?
I think it is something like "AMerican IODine-based ARhythmic ONE"
along the lines of Nystatin (NewYorkSTATeINstitute) or Warfarin
(Wisconsin Agricultural Research Foundation). However I cannot find
any corroboration of my theory.

Names don't have to come from something that has meaning.  There are
companies like the Brand Institute that come up with names just out of
the blue.

Firstly, amiodarone is a khellin derivative originally synthesized by
Labaz Laboratories in Belgium in 1962 (Canada et al, 1983) and was
first investigated for its antianginal properties (Singh, 1983; Canada
et al, 1983; Singh et al, 1989).  As such, it is highly unlikely that
your theory holds up given the fact that it was not discovered in
America.

Secondly, while tradenames for drugs may be acrostic in nature, they
usually are not as stated in the previous comment.  I would be
surprised if nystatin was actually named according to your scheme.

A Harvard Law School article on the etymology of drug trade names is
contained via this link:

 http://leda.law.harvard.edu/leda/data/401/Sun.html

Amiodarone is mentioned, but the derivation of its particular name is
not mentioned; chrislbs-ga is quite correct in that many drug names
are chosen for sound and associations and do not have any particular
meaning.