TS,
in 1768 the buttons are reported to be white metal not numbered. But in the following year they are stated as being of silver, presumably for officers, and numbered - see below. "The coatee buttons had the design of the Star of St. Patrick incised within the circle, above the shamrock was the number 'IV', the whole incised." I got this description from Military Shoulder Belt Plates and Buttons by Major H.G. Parkyn.
There is an excellent book on British uniforms of the Napoleonic period by C.E. Franklin.