Just happened to be skimming thru an old book - 'The Nursery Rhymes of England' Collected by James Orchard Halliwell (whom I've never heard of).  

Found one about the Fiddle: 

Many times poems & rhymes end up song lyrics to wonderful melodies.  

I don't recall any other 'rhyme', than 'The Cat and The Fiddle'. 

...and the only poem - 'The Fiddler of Dooney', by W.B. Yeats: 

WHEN I play on my fiddle in Dooney,
Folk dance like a wave of the sea;
My cousin is priest in Kilvarnet,
My brother in Moharabuiee.

I passed my brother and cousin:
They read in their books of prayer;
I read in my book of songs
I bought at the Sligo fair.

When we come at the end of time,
To Peter sitting in state,
He will smile on the three old spirits,
But call me first through the gate;

For the good are always the merry,
Save by an evil chance,
And the merry love the fiddle
And the merry love to dance:

And when the folk there spy me,
They will all come up to me,
With ‘Here is the fiddler of Dooney!’
And dance like a wave of the sea.

Anyone know of any rhymes or poems about the Fiddle/Violin, Viola, or Cello?