The entry for pig in the Oxford English Dictionary has an entry for the phrase, in a pig's eye:
colloq. (chiefly N. Amer. and Austral.). (in a) pig's eye (also ear, arse) : used as a derisive retort expressing emphatic disbelief, rejection, or denial.
The listed uses are:
1847 J. J. Oswandel Notes Mexican War (1885) iii. 163 Mr. Nicholas P. Trist‥is on his way to negotiate with the Mexican government to make peace. How are you peace—peace in a pig's eye.
1876 Oakland (Calif.) Daily Evening Tribune 17 Mar. 3/7 ‘Bought this mare for $16‥’. ‘In a pig's eye you've bought her for $16’.
1951 E. Lambert Twenty Thousand Thieves 322 ‘Pig's arse to that!’ another voice cried. ‘A jack-up—that's the shot.’
1968 W. Garner Deep, Deep Freeze ix. 110 ‘One stops short of probing the private lives of people for whom one has a regard.’ ‘In a pig's ear!’ she said vulgarly. ‘If duty called you'd have a man under the bed on my honeymoon.’
1992 O. S. Card Lost Boys (1993) vi. 154 ‘She must not have any idea of the effect of her words then’‥. ‘In a pig's eye.’
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.