For the adjective meaning pleasant or attractive, writers from outside North America generally use likeable. Likable—without the first e—is the preferred spelling in U.S. English. In Canadian news publications that make their content available online (which aren’t always reliable for gauging actual Canadian usage), both spellings appear about equally often.
Both forms appear throughout the English-speaking world, however. In current British news publications, likable appears about once for every six instances of likeable. In American publications, where the word in either spelling is less common than it is elsewhere, it is spelled likeable about a third of the time.
Likeable appears to be the older the form. It enters the language by 1700, and examples of its use in early 18th-century British publications are easily found through historical Google Books searches. Most instances of likable that Google finds from this period are actually improperly scanned words like remarkable and suitable. Actual examples of likable become more common in mid-18th-century sources. The American preference for likable gains steam toward the end of that century and steadily becomes more pronounced up to the present.
I would fain know you; for I often hear more good likeable things than it is possible any one can deserve. [1730 letter from the Duchess of Queensbury to Jonathan Swift]
The sexagenary widow remembers that she was handsome, but forgets that it was thirty years ago, and thinks her self so, or at least, very likeable still. [The World, by Adam Fitz-Adam (1755) (British)]
… finally, because it is a very likeable place, being one of the most comfortable towns in England. [Blackwood’s Magazine, volume 38 (1835)]
Altogether Bab was a likeable person in spite of some nonsense, which is more than could honestly be said for her companion. [Our Village, by Mary Mitford (1839) (British)]
The book presents a clear picture of rural life among well-to-do people in Arkansas, and the reader is introduced to several interesting and likable characters. [The Atlantic Monthly, volume 89 (1902) (American)]
Mac had been a stockroom foreman for going on eleven years—a likable sort of fellow, but not the kind that one would ever imagine making a big success of himself. [Popular Science Monthly, volume 96 (1920) (American)]
Few men in baseball are as delightful or as likable as he. [New York Times (1950)]
[H]e was more likeable, more capable of dealing with the country’s problems and had better ideas for keeping America prosperous. [Guardian (1984)]
Davis is likable enough as a lead, with her gentle mien. [Boston Globe (2005)]
If you can get beyond this there’s a lot to like, but likeable characters are not part of the package. [Sydney Morning Herald (2012)]
This ngram graphs the use of likeable and likable in a large number of British texts published between 1800 and 2000:
And this one shows the same in American texts: