I was given a PDF of the following:

OREGON ADMINISTRATIVE RULES
OREGON DEPARTMENT OF FISH AND WILDLIFE
1 – Div. 056
DIVISION 056
IMPORTATION, POSSESSION, CONFINEMENT, TRANSPORTATION AND
SALE OF NONNATIVE WILDLIFE

And it does say Cuban tree frogs are allowed... doesn't mention Barking tree frogs at all, but could they be a subspecies of a disallowed frog?