Fluorescent lamps will work, but they are generally very flat in quality in the fixtures they tend to come in, so you have to make sure that you take steps to counteract this. The flat light is not the best for shooting paintings, as it can fail to show the intricacies of the texture, making the painting seem kind of "blah" and obviously two-dimensional. An oil painting is not only a flat painting; it is a slightly three-dimensional sculpture of sorts. I'd try to make the light from the lamps more directional if you can (but keep the source broad in relation to the subject; moving the light back a ways will make it harsher – which you want – and also will make illumination more even across the surface of the artwork).
Fluorescent lamps also vary quite a bit in color – not only from design to design, but from tube to tube and instant to instant. Make sure your exposures are long enough to capture at least 1/2 complete cycle of the lamps (though at least one full cycle is best). Fluorescent casts vary in color and intensity throughout each cycle, so exposures that last for at least 1/2 cycle allow these variations to average out to appear as a constant color temperature and light output. At 60 Hz, '125 captures about 1/2 cycle, and '60 captures a full cycle. Anything faster, and you are going to get different colors and brightnesses for each shot. Check out this link for a better explanation: http://johnbdigital.com/lenses/fluor...t_lighting.php.
A color meter and a compliment of CC filters will help you out, but most people don't have these items; they are expensive, and somewhat esoteric, especially in the digital age.
And the poster above has an important point. To truly color balance any shot perfectly, there needs to be only one color temperature of light present. For your run-of-the-mill photography, this is not too important. But for copy work, it is very important. Close your blinds/curtains or work in a room without windows, turn off all other lights, and work in an area without colored walls.