Title and lyrics to an old lullaby

I am looking for the title and more lyrics to an old lullaby I used to sing to my children. When I had grandchildren to sing this lullaby to, I realized I had forgotten a lot of the words. I think I might have learned it in school in the 1950's ? Here's the words I can remember:

" So, lulla- lulla, lulla-lulla, bye-bye,
Do you want the moon to play with?
Or the stars to run away with?
They'll come if you don't cry.
So lulla-lulla, lulla-lulla, bye-bye,
In your Mammy's arms be creepin'...
Soon you'll be a-sleepin' ...
Lulla; lulla, lulla, lulla, lulla, bye"