Great stuff Teribus, and thanks. A bit modern for most old folkie's tastes I suppose, as it deals with the whole history right up to the last, but very very interesting.
Keith, your mention of the Warwickshire RHA intrigues me. RHA is usually the abbreviation of Royal Horse Artillery. Was this a local "county" unit? of the Royal Artillery, a militia unit, or what.
"A suit of rifle green" certainly narrows a regiment down. If the song was early 19th century it would have to be the 95th, but as green became common for more rifle regiments as they were raised, the scope widens. By Kipling's time, it could have been one of half a dozen or so.... not including Indian or Ghurka units who may have worn the colour.
Other regiment songs already mentioned elsewhere were
Inniskillen Dragoons / Clare's Dragoons (although I think they were an Irish unit in French service and maybe not a regular regiment - anybody know?)