The use of the word 'ribbit' to refer to the sound that a frog makes came into popular use in the 1930. Before that it may well have been used regionally, but was not a common or well known, as most frogs do not actually make a ribbit sound, chirping, peeping, croaking, and quacking instead.

However, one particular frog does ribbit -- the Pacific Tree Frog. When the Talkies became all the rage, sound men went out to collect sounds for swamps, forests, streams, and rivers. The frog was appropriate for settings all across the world, and was a clear and nonthreatening sound of nature that could be easily inserted without interfering with dialog or plot... but useful though this sound was, the sound effects artists of Hollywood weren't willing to travel very far to get it. So it came to be that the Pacific Tree Frog came to speak for every frog in the world.

It may be interesting to note that the Pacific Tree Frog makes a number of sounds; the ribbit is one of the males' mating calls, along with a crek-ek call. A trilled encounter call is used to warn other males away, and a long cree-ee-ee-eek call is used throughout the year. The females are, as far as I can find, silent.