I can't add much more than is in the BSA book Matt.
BSA originally recommended Kynoch pellets then offered the Adder in both calibres. The Adder name was registered in 1907 and was being advertised by BSA as a diabolo pellet in 1909. It was probably introduced at some point between 1907 and 1909.
Lincoln Jeffries also offered a .22 pellet in a C.1906-08 catalogue but sadly the one I have a poor photocopy of is not dated.
If I had to offer an opinion, it would be BSA or LJ as they offered the first mass produced .22 air rifle. Anything earlier is likely to have been experimental, so I guess the Adder / LJ pellet were the first successful .22 diabolo style.
I would suggest asking John Atkins as I know he is a mine of information on early pellets and I wish he'd write a book on the subject.
John
Currently looking for Baikal Makarov pistols with the following prefixes to the serial number: 98, T01, T09, T21, T22
Prefer boxed or cased but will consider loose examples too.