I have a version very close the one posted by "GUEST,Fleabag" above.

I was taught it in the 1980'ties when I was about 20 by an over 90 year old professor visiting from Birmingham that remembered it from when he was a kid, so it can't hardly be from the last century, but must be even older.

She sat on t'veranda and played her guitar
He sat down beside her and smoked his cigar
She said that she loved him and oh how she sighed
He said that he loved her but oh how he lied
They were to hav'been married but she upped and died
He went to her funeral but just for the ride
He sat on her tombstone and laughed 'til he cried
The tombstone fell over him and splish splash he died
The vicar was passing and popped him inside
She went to the heaven and flip flap she flied
He went to t'other place and frizzled and fried
The moral of this story is you'shd never tell a lie....