I'm really not sure where to post this question. I just know you guys have read everything there is to read, and so have strong opinions about the quality of what is out there. Is there a better place to ask? I'll happily delete and repost there!
What kind of thing are you looking for?
David Cordingly, who is more of a pirate historian, but well regarded in the field, published Cochrane The Dauntless: The Life and Adventures of Thomas Cochrane, 1775-1860 in 2007, which is a general biography. If you're specifically interested in Cochrane's Pacific adventures, Brian Vale has published a few works, starting in 1996 with Independence or Death! British Sailors and Brazilian Independence. Cochrane himself wrote an autobiography, the ... boringly titled The Autobiography of a Seaman, which was republished by Chatham with an introduction by Richard Woodman in 2000.
And of course they're fictional, but the Aubrey-Maturin books by Patrick O'Brian lift many of Jack's adventures from Cochrane, from the Speedy-Gamo engagement to Jack's involvement in South American independence.
David Cordingley has an excellent biography of him, entitled Cochrane The Dauntless: The Life and Adventures of Thomas Cochrane. It's well written and highly detailed, covering the major episodes in his life, from his Mediterranean adventures aboard HMS Speedy through to his support for independence movements in South America. It contextualises his life well, explaining the political and military situations that informed his actions. I'd strongly recommend giving it a read, though I suspect /u/jschooltiger will have his own recommendations.