Green beans are empty calories - meaning they provide none
so a good choice as long as adding more fiber doesn't cause obvious fiber issues - loose stool.
Carrots are good too since unless carrots (all veggies actually) are either cooked well or ground up/pulped, dogs can't digest them / break them down. Anyone feeding whole raw carrots can see them coming out the other end much the same way they went in - so this is a good trick if you want to fill their belly, but don't want any actual digestion going on as no nutrients will be absorbed.
Carrots are not as good a choice as green beans in my view because of the high starch content - carrot can create yeast overgrowth in a lot of dogs resulting in itchiness, gunky ears etc. so be sure your dog does well with them first and watch for yeast symptoms.