Raspberry ( “App. an ellipt. use of raspberry tart") has earlier cites in OED. The putative rhyming slang origin indicates a British origin and the first cite is from A Dictionary of Slang, Jargon & Cant. Embracing English, American, and Anglo-Indian Slang, Pidgin English, Tinkers’ Jargon, and Other Irregular Phraseology. [Edinburgh:] Ballantyne Press, 1889, by Albert Barrere and Charles Leland (the latter an American lawyer who became an authority on English gypsies).
Raspberry, 4a, a derisive sound
1890 in BARRÈRE & LELAND Dict. Slang (1890) II. 171/1 The tongue is inserted in the left cheek and forced through the lips, producing a peculiarly squashy noise that is extremely irritating. It is termed, I believe, a raspberry, and when not employed for the purpose of testing horseflesh, is regarded rather as an expression of contempt than of admiration. 1899 A. M. BINSTEAD Gal’s Gossip 144 A loud and offensive noise, like the rending of glazed calico, made by obtruding the wet tongue between the closed lips, and by low cabmen and persons of that class, called a ‘raspberry’, came from the gallery.
None of the cites seem to be American, unless that ’Gal’ in the title of the second cite’s source is girl, which I don’t think would have been used in England. Gel, yes. Gal, no. But it could equally well be a name. Is raspberry used in the States or is it always the Bronx cheer there?
Bronx cheer: a sound of contempt or derision made by blowing through closed lips, usually with the tongue between; = RASPBERRY 4. orig. U.S.
1929 Collier’s 23 Feb. 10/4 Maxim give him a Bronx cheer. 1932 WODEHOUSE Hot Water i. 21 She told me..that she was through… No explanations. Just gave me the Bronx Cheer and beat it. 1955 E. HYAMS Slaughterhouse Informer 179 That rasping sound variously known as the raspberry or the Bronx cheer.