I know that during the 7 clean days of the nidda / tahara cycle, a woman has to wear white underwear. However, in extenuating circumstances (such as spotting for many weeks), is it ever permissible to wear colored underwear? If yes, what is the source for that leniency?
The short answer is yes there is room for leniency, but as always (and especially in something like this), a competent halachic authority should be consulted.
As I heard it from a rabbi who was offering a review shiur on the subject: The original practice was for a woman to wear libunim, freshly-laundered clothes. The idea was that often garments had all sorts of random stains on them, so a woman might see something and mistakenly think it was a nida problem when in fact it was yesterday's spaghetti sauce or the like. Hence, "wear cleaned clothes."
Over time, the custom evolved from libunim to levanim; not only must they be clean, but white as well. But there can be cases where a rabbi would rule a woman can wear a light color that wouldn't mask or seriously morph any stains, but would avoid the problem of a penny-sized spot on white garments leading to the status of nida.