you might try these things
http://www.leevalley.com/garden/page.aspx?c=2&cat=2,47236&p=46938
What kind of flowering quince is it?
mine died because it was in the shade. Bummer.
Don't get the gel rooting system thing
http://www.leevalley.com/garden/page.aspx?c=&cat=2,47236&p=46944
it is only good with soft cuttings. Hardwood such as quince won't work.

It's just an old heirloom one. It's in pretty heavy shade, and doesn't bloom like many I see, but is reliable.

I'm going to try softwood cuttings again this spring & REALLY work on them.

Most quinces sucker a lot. Just split some off using a sharpshooter and stick them in the ground. I did this to a 'Cameo' with a hand pruning saw when I first took it out of the container. Clipping off just a small portion of the suckers resulted in 12 plants, 9 of which survived from last year to present.

Try your cuttings in June...semi-hardwood. With the high heat and humidity, I usually have good luck with them.
Tim

I'll be patient & wait til June... or maybe May anyway. I think I've tried too early when weather was still cool since they are BLOOMING, I thought it might be the best time.

You might also try some Turkish or Russian quinces. About 3 weeks ago I received a 5-foot tall bare root Aromatnaya quince by mail from Raintree Nursery outside of Seattle. I planted it in a part sun area and it is already leafing out. Raintree says Aromatnaya has a "pineapple like flavor and is sweet enough to eat fresh". Raintree says it is hardy to Zones 5 thru 9. If you are interested in how it is progressing later this year, drop me an email.

I also received from Raintree, Schizandra chinensis (Magnolia vine). Here in Louisiana, we have baystar vine (S. glabra) found in Tunica Hills Wildlife Management Area. Planted the S. chinensis also 3 weeks ago in a dense shade area under an overstory live oak and water oak next to a chainlength fence. So far it has been rapidly growing and has produced a few flowers. Hopefully it can take the extreme south Louisiana humidity as I can use a vigerous fruit producing vine in the shaded portions of my yard. The species will apparently thrive in either full sun or dense shade.

Here is a link that might be useful: Raintree Nursery

zones for planting.
I was lusting after the Magnolia Vine but said, nah, it will die (I've had too many things do that, including a Toyo Nishiki Quince I loved.)
So you think it will grow here? maybe I'll get it after all (of course if you propagate any of it give me a ring! I might have something you want!)