Some cortisol release is obviously needed, but chronically elevated it becomes dangerous. Dietary tyrosine may be able to help. It looks like the dosage is not too high - i.e. about 5g for a human should do the trick.
http://www.ncbi.nlm.nih.gov/pubmed/4068899
http://www.ncbi.nlm.nih.gov/pubmed/4068899