the true origin of the conga are a bit murky, but it first appeared in the USA when introduced there by Desi Arnaz in the 1930s. It's therefore likely that the conga has been danced to tunes that pre-date Little Eva.
The best congas ever recorded (IMHO) were by the Lecuona Cuban Boys, who were Cuban musicians based in Paris in the 1930s. CDs are available - try the usual search methods.
One of the best of them all was a tune called La Havane � Paris.
The conga tune everyone knows (and is probably heartily sick of) was originally called I came, I saw, I conga'd.