ozzy a similar situation happened to me. i'm 20 years old and i have premature graying [it's about 25% right now] so i color my hair every 6 weeks. i permed my hair once and it literally just killed my hair. it also like thinned out my hair. it was a gentle body wave perm too. after 4 months my mom had to just cut the permed parts off. i had boy short hair for a loong time. it's finally grown out and i promised myself never to do that again.
however my mother perms her hair [been doing so for years] and her hair is just fine. she doesn't color her hair though.
overprocessing and too much chemicals to the hair in my opinion aren't great.
i'm back to sponge rollers before i go to sleep for a curl. takes 5 minutes to put the rollers in but don't have to worry about frizz, roots, or my hair being fried.
My DH gives me a perm ever 6 months or so. I like the Precisely right perms. Have never had a problem, and I color my hair. The trick is in the roll-up. If you roll it too tight, it will break as the curl sets.
A better idea may be large rollers or finger curling - neither will cause as much damage to your hair as a perm would, and if you don't like the way it looks, you just have to wash your hair to take the wave out.
If you're blow-drying your hair every morning, then trying rollers/finger curling a few times won't add too much time to your routine. If you can find yourself a portable bonnet-type hairdryer, you may find you even save time, because your hair can dry while you're running around doing other things.
Don't laugh too much at the idea of a bonnet-dryer either, they're becoming more popular again because they're more gentle on the hair than a hand-held dryer, or heated rollers. (the heat isn't directed right at the fragile ends) You can also use them to provide heat for deep-conditioning treatments
If you still want a perm, you'd be best off waiting about 6-8 weeks since your last colour, and getting a few deep-conditioning treatments in the meantime. You should also wait at least 3 weeks after the perm to dye your hair again.
Before you have the perm done, get your hairdresser to do a test curl - it's where one small piece of hair is curled to see how the perm takes, so you don't find all your hair ruined if the perm doesn't go well. If the test curl turns out fine, you're all set
If you find you have visible roots in the meantime, there are ways of covering them
If you dye darker, a "lasts up to 6 washes" temporary dye without peroxide or ammonia will do it - all they do is deposit pigment onto the hair, so they won't damage it.
If you dye your hair lighter, or redder, you can get away with only dyeing the roots at your parting and hairline, provided the perm doesn't also cover those areas.