I don't know about thornless -- I never pay attention to that -- but for size and consistent re-bloom, I'd recommend the true Polyanthas.

Jeri

'Gruss an Aachen' and 'Pink Gruss an Aachen', often sold as 'Irene Watts', are excellent small roses. They have a few thorns, but not many.

The miniature 'Cinderella' is completely thornless. 'Marie Pavie' has pretty much thornless stems, but does have those tiny back of the leaf prickles.

Don't underestimate the intelligence of children. They quickly learn which plants it's best not to fall into. My brother and I practically grew up on our grandparents' dairy farm negotiating barbed-wire fences and blackberry brambles.

Oops. Forgot to mention. They belong to the polys that Jeri recommends, but check out the Cecile Brunner clan (Mlle Cecile Brunner, White Cecile Brunner, and Rita Sammons.) Those are smallish and low on thorns.

Some years ago, I consulted with a local botanical garden on a selection of small roses for a Children's Garden.

I asked them whether thornlessness was a priority.

They said, no. It was not.
They felt, in fact, that it was best children learn early that some plants have thorns or prickles.

I was reminded of my younger brother, who learned the hard way that you should not insert toy knives into electrical outlets.

Jeri

I have over a dozen Marie Pavie. It is smallish and nearly thornless, if not thornless. It smells wonderful and blooms all the time, hardly gets disease. It's really easy to root cuttings, too. It does tend to hang on to it's flowers even after they fade, but deadheading is not absolutely necessary as it keeps on blooming.

Austin's Pretty Jessica is a nice little bush with plenty of blooms.

Specific polyanthas: Borderer, Lauren, Anda and White Pet.

Sweet Chariot is a big miniature for me. I grow it in a pot.

Sherry

Here is a link that might be useful: If only sweat were irrigation...