Try these:

Up a lazy river by the old mill run,
A lazy, lazy river in the noon day sun,
Linger in the shade of a kind old tree,
Throw away your troubles, dream a dream with me.

Up a lazy river where the robin's song
Awakes a bright new morning as we roll along--
Blue skies up above, everyone's in love,
Up a lazy river, how happy you will be,
Up a lazy river with me.

Roger and I are close in all but the third and fourth lines of the first part, and a word here and there. I guess my version has the couple together overnight (strange, since I learned it in church camp in the 40's)