According to this excellent article on the history of the regiment they were called Blues from the 1740s before they had a blue uniform in 1760 and it may have been something to do with the Blue Mountains.
They were a smart and practically attired unit with a simple cartridge box described in Redcoats Yankees and their Allies as a straight wooden block with two rows of holes, one 12 one 11 - with a 2 1/4'' linen strap attached.
They were immortalised in song
Should foul misrule and party rage
With law and liberty engage,
Push home your steel, you'll soon review
Your native plains, brave Jersey Blue.
Further study - print by Company of Military HistoriansOrigin and Sketch of the"Jersey Blues"
Originally published in the "Proceedings of the Historical Society of New Jersey"By WILLIAM H. BENEDICT, New Brunswick, N. J.