Forcing an organism to evolve/adapt by exposing to radiation, and stressful environment. What organism shal I use?

Would UVB be a reasonable source of ionizing radiation? Such bulbs are available commercially, a great many people have them on aquariums in UV sterilizers, I have designed UVB sterilizers for the company i worked for back in the day, I think Arete would be your best source of info on how to use them for your purposes.

I was going to put this forward but refrained because anything that causes mutagenesis in a specimen will also potentially do it to the operator and also there's the risk to eyes to think about as well.

 

Abstract

Global atmospheric changes such as depletion of ozone in the stratosphere are thought to lead to increased levels of ultraviolet radiation on earth. This can have adverse effects on human health, and long-term effects of ultraviolet light on the eye are of increasing concern. Ultraviolet light exposure to the eye has been associated with cataract formation and retinal degeneration. In both cases, it is hypothesized that ultraviolet light can initiate formation of free radicals, which can cause protein modification and lipid peroxidation. Several procedures can be recommended to prevent ultraviolet light damage to the eye, such as the use of suitable protective glasses when outdoors.

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1568237/