I doubt they have ever been bred in captivity. The babies are pelagic. Even farmed ones are just collected from the wild and grown. They certainly wouldn't be breeding in the awful little tank above.
I believe Tennessee Aquarium is the only place in the US with multiple individuals of the species. From what I can tell they’re kept behind the scenes but one is occasionally brought out as an “ambassador.” TA does a lot of work with hard-to-breed species but their specialty is turtles and fish, not coconut crabs.