I want to say that the full swim for two of us with an upgrade special was about $125 each, but I honestly don't remember exactly. It was approximately 30 minutes in the water with a small group of people (I think our group was 6 people) and two dolphins, and it included a dorsel-fin pull, nose push, petting, etc. It was really great.
I would guess that the regular price for the same encounter now would be about $200. They do offer specials through the various resorts at various times, so I'm guessing that's why they don't post the prices.
If you're worried about having enough cash or room on your credit card, I'd suggest calling the resort directly a couple days ahead. That way, they might have a better handle on what deals may be offered and what the current prices are.
I do remember a few people saying that it was far more reasonably priced than in the U.S., and I personally was impressed with the professionalism, "humane-ness" and cleanliness of the facility.
I think there are other places where you can get information, but it takes some researching. Also, I think I've seen certain tour groups offering prices for a Dolphin Cove tour. Those often include another attraction like Dunn's River Falls.
Hope this helps! I'll update if I find other helpful links.