How about Bonny at Morn. It's a beautiful Geordie lullaby. Otherwise a song that I started singing when I was about 16 was A maid Going to Colmer. Don't know if that's the proper title or who originally sung it as a friend taught it to me. Maybe someone else has more info on it. It's a really beautiful gentle song as well. I can give you the lyrics and maybe someone else can advise on how to get hold of the tune?

A Maid Going to Colmer

A maid going to Colmer her markets to learn
to sell for her mammy three hanks of fine yarn.
She met with a young man along the highway
and it caused this young damsel to tarry astray.

Sit down beside me I mean you no harm,
Sit down beside me this new tune to learn,
Here are three guineas you mammy to pay
if you'll lay by your yarn till the next market day.

Well this maid she's gone home with the words that he'd said,
The air that he played her still rang in her head.
She said I'll go find him by land or by sea
till he learns me the tune of the next market day.

Sit down beside me I mean you no harm,
Sit down beside me this new tune to learn,
Here are three guineas you mammy to pay
if you'll lay by your yarn till the next market day.