Hi, John. Mostly similar to yours, but the version I learned as a kid has an extra couplet in the middle and another at the end.

Good morning, Mr Murphy. God bless your heart and soul.
I tried to fuck your daughter but I couldn't find her hole.

At last I found her hole underneath her frock,
Then, damn it, Mr Murphy, I couldn't find my cock!

At last I found my cock underneath my hand,
Then, damn it, Mr Murphy, I couldn't make it stand!

At last, I made it stand as straight as any pin,
Then, damn it, Mr Murphy, I couldn't get it in!

At last I got it in and wiggled it about,
Then, damn it, Mr Murphy, I couldn't get it out!

At last, I got it out all rosy red and sore,
Then, damn it, Mrs Murphy, the bugger wanted MORE.

I gave her more and more, as much as I could stand,
And now she's wheeling babies up and down the Strand.