Probably not this one, which started life as a street rhyme, and I believe was extended by Robin Hall and Jimmy McGregor:

THE SACK 'EM UP BOYS
Chorus
Up the Close and doon the stair,
But and ben wi' Burke and Hare,
Burke's the butcher,
Hare's the thief,
Knox the boy who buys the beef.

Hurry doon the Castle Wynd,
Look before and look behind,
There they wait tae tak yer life
And sell ye fur the surgeon's knife….

Auld or young or dark or fair,
It maks na mind tae Burke and Hare,
While Dr Knox peys oot the tin,
They'll sack 'em up and bring them
in….

Reekie's rows are dark and drear,
Reekie's vennels reek wi' fear,
Mind yersel gaun doon the stair,
Fur fear ye meet wi' Burke and Hare…