Where do you start? Is it really possible to find paint products?
The good news is that it is possible to buy eco paint. There are quite a few companies claiming to provide environmentally friendly paint. Not the cheapest alternative to conventional paints, but then that's not the main priority when you're trying to avoid harming the environment or your health.
For example
Tikkurila a Nordic paint company focusing on eco friendly waterbased low VOC paint products.
Earthborn established in 2002 who provide eco alternative to conventional paints even listing the ingredients on the side of their tins.
Hemway Chalk paint for all your shabby chic furniture projects
If you are not ready to pay for true eco friendly products then maybe focus on waterbased paints instead of oilbased. At the very least this is a step in the right direction. As a decorator of over 23yrs I can honestly say converting to waterbased products has really aided my health. The strong VOC's can really affect the respiratory system, avoiding them as best you can will save you in the long term.
Whatever the reason your looking, hopefully this has given you a head start.