Here's the way I learned it from a recording made in 1941 by my own dearly departed father in one of those "Sing It Yourself" recording booths at Coney Island. :)

I Married My Wife

I married my wife in the month of June,
Nickety, nackety, now, now, now;
I courted her home by the light of the moon,
Nickety, nackety, now, now, now.

She combs her hair just once a year,
Nickety, nackety, now, now, now;
But just the same I love the dear,
Nickety, nackety, everything's frolicky,
Nickety, nackety, now, now, now.

She washes the kids in the kitchen sink,
Nickety, nackety, now, now, now;
She makes the black ones all turn pink,
Nickety, nackety, willopy, wallopy,
Nickety, nackety, now, now, now.

The bridle and saddle lie on the shelf,
Nickety, nackety, now, now, now;
If you want any more you can sing it yourself,
Nickety, nackety, everything's frolicky,
Nickety, nackety, willopy, wallopy,
Nickety, nackety, now, now, now.