I'm sure you have already found this information, but thought I'd pass it along just in case:
Parents of Sheriff William Brady are:
John and Catherine Brady, William was born August 16, 1829 at Cavan, County Cavan, Ireland. He left Ireland for America in about 1851. He enlisted in the Army 7/11/1851 and left the Army in 10/1866. He was married to Maria Bonifacia Chaves Montoya on November 16, 1862. There is more information posted at the following site, including photos: http://www.angelfire.com/mi2/billythekid/brady.html
Fair warning, it basically calls him corrupt, etc., but it is informative as far as the above info.
Also, please email me, as I have a Brady in my line that I can't find anything on, maybe you can help.
Thanks and hope the info helps firstname.lastname@example.org