Here's the tune. I used ABCMUS to convert the Digitrad SongWright file. I checked it with the tune printed in "Songs of Dublin," and it seems to be pretty much the same tune.
-Joe Offer-

X:1
T:The Finding of Moses
Z:Author: Zozimus?
M:4/4
L:1/8
Q:100
K:D
AD-FA- BA2A-|FDFA3/2B/A3|AB2E EF2D|FAFE FD3|
W: On Ay- gypt's banks con- ta- gious to the Nile, The ould Pha-roh's daugh- ter, she went to bathe in style.
AD-FA- BA2A|FDFA BA4BBE EFFD|FAFE FD3|
W: She took her dip and she came un- to the land, And to dry her roy-al pelt she ran a- long the strand.
Ad2c- BAF3ddc BA4-ABB BB-cd-|BABA GF3|
W: A bull- rush tripped her where-u-pon she saw a smi-ling ba- by in a wad of straw;
ED-EA- BA2A|FDFA BA3|ABBE EF2D-|FA/A/FE FD3|
W: She took him up and says she in ac- cents mild, "Oh ta-ra- na-gers, girls, now Which of yis owns the child?