'Transatlantic Voyages and Sociology: The Migration and Development of Ideas' By Cherry Schrecker (Google Books) gives the date as 2 January 1882, and the actual quote as
> I have nothing to declare **but** my genius
(My emphasis)
Schrecker cites the book 'Oscar Wilde' by Richard Ellman (1988) and another source as 'Bradbury 1995', but having no access the the actual Schrecker book, this reference remains sketchy.