More on the lines of Be kind to poor Nelly, IIRC.

The earliest Give My Love to Nell reference I can find offhand is to a songbook of 1931: Walter Peterson, "The Kentucky Wonder Bean": Sensational Collection of Mountain Ballads and Old Time Songs:  Old Time Country and Western Music Souvenirs and Song Books.

However, Bruce E. Baker's  More Than Square Dance Music  implies that the song was known at least as early as 1915, and perhaps before.  I can't say that it strikes me as in any way Irish, or particularly old, but one never knows.