Pretending to be interested in something else seems to work as derway suggested, especially with turtles, who will sometimes come over to see what you are looking at.
Don't look at your subject directly and don't make any sudden movements. You are hundreds if not thousands of times bigger than most of your subjects so be nice and calm and friendly. Your eyes are a major source of deterrent to animals so don't glare at them. The housing itself could be seen as a huge monocular monstrosity itself and fish do not like to be eyeballed.
As ATJ said, understand the behavior of your quarry, know their comfort zones, use the zoom to get decent framing if proximity is an issue and utilise the cleaning station stupor to get that extra couple of feet closer in.
Go somewhere the fish are used to divers. Blue Corner here in Palau is awesome for that. There can be 1000 divers there each day during busy season and the resident fish do tolerate them much more than at other less frequently dived sites, especially the sharks.
Control your buoyancy and control your breathing, if you can't control your buoyancy, you shouldn't have a camera. Simple.
Trickle your exhalations, being calm helps infinitely.
If you want to come to Palau and see the Mantas, don't come in busy season as there are easily 20+ boats at German Channel every day, the frenzied hordes of camera wielding tourons have most likely already chased off anything/everything of interest.
Just my $1.37 worth
Richard (Anthropomorphism) Brooks