As a History Canada series, "The Curse of Oak Island" likely derives a good deal of its budget from the production infrastructure of the show itself, meaning both History and production company Prometheus Entertainment (via IMDb) most likely pitch in with funds to pay for the cast, crew, and equipment. Typically, the distributor ends up shouldering most of these costs after everything shakes out, which is likely the case here.
Moreover, as owners of a 50% stake of Oak Island Tours, Inc., the company that owns Oak Island, Marty and Rick Lagina fund a good deal of the Oak Island drilling and digging operations themselves (via History). Remember, they might still be doing a lot of this treasure hunting even without the TV deal. The whole story depicted on the show began when Marty and Rick bought the stake so that Rick could pursue his childhood dream of finding the treasure. That dream is surely no dramatic creation of TV execs at History or the development folks at Prometheus Entertainment. Craig Tester also apparently acts as a financier through Oak Island Tours, Inc. (via InstaGeeked).
Much of the money spent on the Oak Island search also comes from local sponsorship. Nova Scotia Business Inc (NSBI), an agency that helps businesses in the province of Nova Scotia grow, has contributed a lot of money to "The Curse of Oak Island" through its Nova Scotia Film and Television Production Incentive Fund (NSFPIF). Figures have included CAN$1.9 million for Season 5 (via TV Over Mind) and a whopping CAN$3.97 million for Season 6 (via Monsters & Critics). That certainly helps defray a lot of the costs that would otherwise be reflected on History's balance sheets.
According to Showbiz CheatSheet, other potential funding sources for the show include Oak Island tours and government grants.
