Depends on what you are looking for and when you will be here. In terms of duck hunting, the best we have is seaducks, you'll see plenty most days but getting the weather to cooperate can be a challenge. Seaducks here are primarily eiders, slightly fewer oldsquaw while scoters do not constitute much of the daily bag. You can try this fellow on Fogo Island on the NE coast http://www.openboatoutfitters.com/
. From St Johns that would take a 3.5-4 hr drive and a ferry crossing. Season runs from 4th saturday of Nov to last day of Feb for sea ducks and limit is 6 per day. Again the weather is the real deciding factor, not presence of birds.
As for other duck and goose hunting, it can be hit or miss, mostly miss. As others have said waterfowl hunting is not as productive here as on the mainland, lots of habitat and water but curiously not covered in ducks. Season starts in Sept and runs to mid Dec for inland ducks and geese. Early season expect black ducks, canada geese and GW teal, as it progresses divers become more common, mostly mergansers and goldeneye. Given the sporadic hunting most outfitters do not offer dedicated waterfowl hunts, tho some offer it as a side dish. Once your cousin gets situated here it shouldn't be much of a problem to find a local willing to take you out. Also, once he becomes a resident he'll be able to participate in the Turr hunt, 20 birds a day for that, tho non residents are not permitted.
Also, as others have said you may want to check into other Atlantic Provinces for waterfowl opportunities, sea ducks you can easily find in Nova Scotia and New Brunswick while PEI will give good goose and puddler action. In NS check Goldeneye guide service, Brian Mason at email@example.com
and for PEI you can try malpeque canada goose outfitters at http://peihunt.webs.com/