Can antibiotics give a toddler bright green stool?

Yes. If your toddler is also starting to develop loose stool or even diarrhea, yogurt (if they will eat it) can help. Antibiotics alter the normal bacterial flora found in the intestine, and yogurt can help start to restore balance.
Possibly. Green stools are usually due to bile--from the gallbladder--which has traveled too fast through the intestines to be broken down. Antibiotics will alter the bacteria that normally live in the gut and may speed up how fast stools pass through as well--so the "undigested" bile may give stools a green color.