Argentina was, like Britain, not directly militarily supported by any other nation (not with troops, that is). However, Peru was a very open ally of Argentina, and supplied large amounts of weapons and planes. Libya was also an active supporter, sending some 60 missiles to assist the war effort. Venezuela and Guatemala were somewhat vocal supporters, and offered to assist Argentina later in the conflict.
On top of these specifics, the Non-aligned movement did throw in its political support for Argentina, and much of Latin America backed Argentina. Unfortunately, Argentina lost some support it hedged its bets on, such as the continued support of the USA and France in supplying planes, and more importantly, exocet missiles.