R Doradus, My Doradus, Your Doradus, Their Doradus... :^)
El Doradus.................
But -us is very unusual for a Latin genitive and appears actually to be a Greek genitive.
The constellation is Dorado in the nominative case.
Bennett's New Latin Grammar, 28, cites the Greek third-declension proper noun Dido as having a genitive form Didus. So that seems to be what's going on with Dorado/Doradus.