Here's 2 threads with some variants on this song: Two Sisters (Child #10) Variants dulaman/two sisters

Here's the version of "The Two Sisters" that I learned from Touchstone; it sounds American, but someone told me that Claudine and Triona got it from Clannad...This may be the one you're looking for.

There were two sisters, side by side
Sing aye-dum, sing aye-day
There were two sisters, side by side
The boys are bound for me
There were two sisters side by side,
The eldest one to Johnny cried

I'll be true unto my love,
If he'll be true to me

Johnny gave the youngest a beaver hat
Sing aye-dum, etc.
Johnny gave the youngest a beaver hat
The boys are bound...etc.
Johnny gave the youngest a beaver hat
The eldest didn't think much of that, oh

I'll be true...etc

(repeat all lines in italics for each verse)

Johnny gave the youngest a gay gold ring...
He didn't give the eldest anything.

As they went a-walking by the foaming brim
The eldest pushed the youngest in.

Oh, sister, give to me your hand
And you can have Johnny and all his lands.

Oh, no, I'll not give you my hand
And I'll take Johnny and all his lands.

So down she sank and away she swam
Until she came to the miller's dam.

The miller, he took her gay gold ring
And then he pushed her in again.

The miller was hanged by the mountain stead
The eldest sister was boiled in lead.