Easiest way to tame weak carnivorous (dimetrodon, for exemple) :

1rst : build a trap, to let your beloved victim falls in

2nd : get an agressive, (but the weakest you'd find) dodo on your shoulder

3rd : start the knock out process, for the next taming

4rth : as soon as the victim's HP are too low to keep the knockout, release the dodo

The the dodo would attack directly the tame, so you really don't want a high level one ;

At the really 1rst dodo's attack, you'd whistle passive

By this way, the tamin would agro on the big bird, eats it, heal back, while you'd keep knocking it