Tame a kaprosuchos and swim to one of these bad boys and do it's alternate attack it will grab it in it's mouth. walk onto the shore where its safe and have another person feed it while in the gators mouth (if you unmount it drops it) it wont attack or die because it's technically not on the shore.
Get a basilosaurus and get the manta you want to tame, agro it to the balsilo and you will be able to tame the manta since its attacking the basilo instead of you. (The basilos food will drain quickly so get it some food)
Never I mean never bring your high level Rex in the water in the center map because like 20 of these things killed my level 171 Rex after I tamed it and was going to lava island and my Rex fell off the boat.
When taming place a stone foundations with doorframes on all sides except for one in the water with doorframes just under the water, aggro the manta in the spot and place a doorframe to lock it in. You can feed it while it aggro to a wall for safe taming.