I've altered the first verse a little bit and put in some punctuation. The third verse is fairly straightforward and is the first to have a end-line rhyme. Otherwise I like the way the rhymes and part-rhymes are scattered through the poem a bit like birds around the garden.
There's a little round robin
and a really round wren.
The wren is rounder than the robin
but the robin's redder than the wren!
Some say the robin is a sweeter tweeter
but the wren's the doyen of song.
She's a round yo-yo of feathers;
she's a little bomb of sound!
The blackbird is a handsome fellow
And his song is pretty good.
The thrush can sing a mellow ditty
When she's in a skittish mood.
Now I just need a way to finish it off!