I am searching for a site for furnished apartments in Tuscany for 1-2 weekw
It may not be what you're looking for, but Agriturismo Cretaiole near Pienza was wonderful. Check out reviews on Trip Advisor.
If you are open for a hotel option, the Hotel San Lachese in Poggibonsi is wonderful. Family owned. Good food. Convenient distance to Florence and the hill towns. We had a tour bus, so don't know how convenient other transportation is.
You could try the site VRBO, I think it stands for vacation rental by owner. Or try Parker Villas, they have a lot of homes but there are a lot of apts. or shared properties as well. I've used them both. Parker may be a little more pricey because there is a middle man involved but they also put their reputation up with the referrals. It's all what you are comfortable with.
You should also check out Rentvillas.com. We had very good luck with them.
We rented through this agency: www.interchalet.co.uk They have a really good search engine that let's you customize quite easily the kind of appartment and location you are interested in. Lots of options in a variety of affordable prize ranges.