Hmmmm. I have never been to Denaru, so I am going out on a limb here. I think because it typically caters to tourists, you might find some lowish grade kava offered for the "cultural experience". I would be surprised if there's genuine kava bars on the island BUT you may find hotel workers sitting around a bowl at times. I've seen this lots around Nadi. I am sure they would happily invite you in to try some. If that fails, I would ask the restaurant/front desk staff, and I'm sure some of them will point you in the right direction.
I never looked specifically for kava on sale in Fiji, but I saw a reasonable amount in Lautoka market on a Saturday morning. Lautoka is bigger than Nadi anyway, so it might be worth a trip up there (hire a car if short of time; the bus will take forever, though may be more fun
)