Any ideas for getting bright orange vomit stains out of very light coloured carpet?

I have used the commercial carpet cleaners (the spray foam in a bottle w. a scrub brush) for things like doggy diarrhea and food stains on our cream-colored carpet in the dining room (I know, what was I thinking when I bought a rug for the DR in such a light color?!) I have found these cleaners, although very chemically, work pretty well.

The trick is to wipe off as much as you can of the stuff with paper towels (or rags, or watever). Try to absorb as much of the liquid in the stain as possible. Then use the foam, scrub well, let it dry, vacuum. Reapply again if you must.

Also, oxi-clean mixed with water can also help. I have done a combination of both techniques (switching off between applications) with ok results.

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Woops, I just realized you posted this in the "green" section and my recommendations are not very eco-friendly!

I might resort to them, if needed, so I'm glad to hear that they work.
I was looking for something more natural because I'm sensitive to chemicals, so even if I can get someone else to do the cleaning, I don't want the fumes in my bedroom. Also, dh is out of town and I have sick kids home, so I can't run out to the store today. Was hoping to find a trick that used stuff I have in the house already - baking soda, vinegar, peroxide laundry bleach (liquid). I guess the peroxide laundry bleach diluted with water might work.

I have used regular peroxide and oxy clean. adding some essential oils like lavender, lemon and/or tto will help with smell and also anti bac/virus whatever.
You might have to leave the oxy or peroxide in for a while and then scrub and repeat again.
sorry to hear the kids are sick:(

If you have some bentonite clay (calcium bentonite) mix about 1/2 a tsp with raw honey or applesauce whatever you have at home and give them a spoon. It is amazing and really works with "tummy bugs" has the ability to absorb toxins safely :)
give them something to drink right after since 1) even though it has no taste it has a clay texture and some kids don't love it and 2) it is good to be hydrated when sick!

I'm not smelling anything, which amazes me, but might be more due to my allergies than actual lack of smell. Or, it might be that I covered the patches until I could wash them well. I'm pretty certain all that is left is staining and not actual vomit.

B"H no more vomiting since the two episodes this morning. Now, one kid has high fever, but advil helped and he's managed to eat a couple of slices of bread. Older dd feels too uncomfortable to even drink, but no fever, so until she can sip water without cramping, I'm not letting her eat. I'm hoping that will encourage her to drink, because I think the cramping is probably being incredibly sensitive rather than violently ill.
B"H my 9yo ds is home from camp, and he was really happy to play with the baby, so I'm getting a few minutes to myself!

oy, R"SH!

Some chamomile tea, maybe, for your dd?

B"H, everyone was feeling OK today. DD1 was feeling well enough to come clothes shopping with me. DS1 was tired but not sick. DS2 was no longer feverish, though his stomach was still a little "off" - he didn't finish his supper - but that's normal for him. The baby seems to have had a better day, took two naps in the car, and went to bed at a reasonable hour without too much protestation.
Now to get the boys in bed, and I can work on those stains again!