Get a photographic 18% gray card. Use it to set both the exposure and white
balance. Your light source may be causing glare which you can mitigate by
using a polarizing filter on the camera lens and positioning the lights
properly. You could also bounce the light off a white surface (just make
sure it doesn't catch fire) or through a white material.  Ensure that your
lighting is even. I don't know what the spectrum is for halogen, as long as
it's continuous you should be OK.

Have you (or even can you) set the White Balance of your camera from
AUTO to TUNGSTEN?  Halogen lamps as well as most any filament lamp have
a different color spectrum than daylight: much more red and yellow.

Auto White Balance depends on having a variety of colors, plus black and
white, to work properly.  If you have a scene where on color
predominates like your mostly red paintings , then the white balance
gets "confused" and makes a mistake in the color balance.  In your
situation it is better to set the White Balance manually, depending on
the predominate light source.

If your camera can "lock" the Auto White Balance once a reading has been
taken, then hold a large white poster card in fron of your paintings,
take a reading, "lock" the White Balance, remove the card, and take the
picture.

The other solution is to get an 80A filter and put it on or hold it in
front of your camera lens.  This will adjust the spectrum of the
halogen light to get close to standard daylight.  Or you can get light
balancing filters from a movie or theatrical lighting supply house to
put over your lights.  Rosco Industries (www.rosco.com) or Lee Filters
(www.leefilters.com) are two companies that make them.  For Rosco, you
want Cinegel #3202 Full Blue (CTB).

I suppose you are putting the pictures on the WEB to show
prospective customers, so the color veracity is going to
be a problem exasperated by the monitor and conditions
of the person viewing the images on his own computer.

Given this you could probably give more of an idea of
the "spirit" of the paintings by buying Paint Shop Pro
or equivalent and playing with the contrast, brightness
hue etc. settings. It is probably a cheaper alternative
to buying more lights lenses or digital camera. Remember
that images for the WEB are of pretty low quality because
they have to be small in pixel and byte terms.

Just an idea....

--
http://www.ransen.com/
Repligator - Easy graphics effects
Gliftic - Easy decorative tilings

Thanks for your replies - my camera is pretty low-tech, so all I can
do is set the white balance to 'lightbulb', which doesn't help. Sounds
like filters may be the way to go.