S. Worthen | Weblog

To answer my own question, I found something here on the subject:

"DOLLARS TO DOUGHNUTS (or donuts) – “The almost forgotten terms ‘dollars-to-buttons’ and ‘dollars-to-dumplings’ appeared in the 1880s, meaning ‘almost certain’ and usually used in ‘I’ll bet you dollars-to-buttons/dumplings.’ They were replaced by 1890 with the more popular ‘dollars-to-doughnuts’ (a 1904 variation, ‘dollars-to-cobwebs,’ never became very common, perhaps because it didn’t alliterate).” From “Listening to America” by Stuart Berg Flexner (Simon and Schuster, New York, 1982)."