This Wikipedia article says that "in a pig's eye" is rhyming slang for "lie", but I'm not convinced. The article also claims "in a pig's bottom" exists as a variant – but I doubt that's ever had any meaningful level of currency, which is another reason I don't much trust the author.
There might be some element of alliteration (also with "Pigs might fly"), but it doesn't seem like the kind of rhyming slang I'm familiar with.
Can anyone either substantiate the Wikipedia article, or give a more convincing etymology?
EDIT: Soddit – the Wikipedia page lacks citations anyway, so I just changed it.
Best Answer
The entry for pig in the Oxford English Dictionary has an entry for the phrase, in a pig's eye:
The listed uses are:
So the first recorded use was in 1847, and by this time the OED says that it was already being used as a "derisive retort". As the phrase is chiefly from North America and Australia, it is highly unlikely that this is Cockney rhyming slang. However, the article does say that "in a pig's arse" is an actual variant. One of the included uses (see 1951, E. Lambert) uses arse instead of eye.