Carry it to a pre made taming cage with an argy (the argy will be able to gank hits whilst carrying easily) then drop the Baryonyx in, and ez tame it. Also, don't use fish meat li,e everyone else is saying. Just use regular kibble.
This dinosaur is a very intricate but interesting dinosaur to get. I did find it near the shore line as it had seen me and wanted to eat me. However I had 5 tranq arrows which you can get at lvl 21. I shot all 5 and he fell to the ground. Very good dinosaur to tame especially in the water. It beats anything in the water even with its stun strike. I recommend using this dino to fight. I have one named Juju. One like equals One love for Juju