On a serious note, a search of several online archives turns up no evidence of a tune called "reilly's daughter" or "riley's daughter" but a tune called "Wrecker's Daughter" can be found in the library of congress as sheet music starting around 1840. Wrecker's Daughter has portions of the modern "Reilly's Daughter" in it and one of the earliest versions was published by Riley as a pianop arrangement purportedly based on the original German text. Other versions were commonly described as being based on music played by marching bands, and Wrecker's Daughter is still alive in much it's original form in the repertoire of fife and drum corps players. Riley also published several collections of flute tunes in the same era.

Here's a link to the library of congress Wrecker's Daughter sheet music on line:

http://memory.loc.gov/cgi-bin/query/S?ammem/mussm:@field(TITLE+@od1(The+wrecker's+daughter++))

And here's an ABC version based on a fifer's book, "American Veteran Fifer", published circa 1905:
X:121
T:Wrecker's Daughter *?
B:American Veteran Fifer #121
M:2/4
L:1/16
Q:1/8=240
K:D
aaa z aaa z|aaa z aaa z|E2A2 d2de|d2c2B2A2|bbb z bbb z|bbb z bbb z|B2d2 g2ga|g2f2e2d2|ccc z ccc z|ccc z ccc z|A2ce a4|A2ce a4|f2e2c2f2|.d3 z .d3 z|d6 z2:|e2e2f2e2|
c2c2d2c2|B2B2f2e2|c3GABcd|e2e2f2e2|B2B2 f2e2|A2 z2a4:|F4 A2d2|F4 A2d2|G4 B2d2|F4 A2d2|E4 G2B2|A4 d2f2|e2^gg g2g2|a2 z2 a4|f4 A2d2|f4 A2d2|G4 B2d2| F4 A2d2|E4 G2B2|A4 d2f2|e2AA B2c2|d2 z2 d4:|

Anyway, the point is that Reilly's Daughter may (or may not) be derived from "Wrecker's Daughter". Where the heck "Wrecker's Daughter" originated I am not sure - perhaps there was some military figure nicknamed "Wrecker"???