I was looking through a book about Indian English (Sahibs, Nabobs, and Boxwallahs: A Dictionary of the Words of Anglo-India) and I noticed the following definition (edited lightly):
Cherry-merry: Baksheesh. A present of money. [19th century; etym. obscure] [OED; Partridge, Dict. of Slang etc. 1979]
Cherry-merry bamboo: Literally, ‘a present of bamboo' : A thrashing; a sound drubbing. [19th century] [Partridge, Dict. of Slang, 1979]
Most of the definitions provide a concise etymology, but this one didn't. So I referred to the given source, Partridge, and I couldn’t find any extra information. (I don't have access to the OED, but the entry implies that Oxford doesn't know either.) It’s also in a number of other dictionaries, but none of them offer any clues as to the word’s etymology. 'Cherry-merry bamboo' is present in many dictionaries, too, and one of them notes that the 'cherry-merry' part is likely used ironically.
'Cherry-merry' seems to have a couple of other meanings, like 'convivially tipsy' and (somewhat doubtfully) 'girl who just had sex for the first time'. Some of the entries hazard etymologies for the other meanings, but they're pretty useless when it comes to the one that means 'tip.'
The Oriental Interpreter suggests that 'cherry-merry' is used "chiefly, if not solely," in India, too, and it is included also in an 1891 dictionary of Australian slang. Unfortunately, as I realized later, it's under the Anglo-Indian slang section, so it's actually not that helpful.
Wiktionary, linked above, notes that it's obsolete (I agree), and provides the quotation:
"That not proper business," said Croke Sahib. "What for I give cherry-merry?"
1858, Michael Rafter, The Rifleman (page 232)
I also found it in a 1999 play, where one character calls another a "towsing, cherry-merry bamboo!" The play takes place on the Indian Subcontinent, though. Venturing into the non-English results, one dictionary defines 'cherry-merry' as 'Geschenk in Geld', and says that 'cherry-merry bamboo' was actually Pakistani slang.
So what could be the origin of 'cherry-merry' to mean 'tip,' or 'baksheesh' in 19th-century Indian English slang? And are there any citations of it being used organically outside of the Indian subcontinent?