My children, both US citizen, age 5 & 8, will join me in Geneva, where I will be working for international organization on CDL. I'm wondering if they will be able to apply for citizenship after living in Switzerland (probably with Ci-permit during these years?) for certain years?
No. NGO permits don’t qualify for Swiss citizenship. The years spent on them might, but they’d need to find jobs here giving them a B permit, then after a few years they could apply for a C permit if they meet the qualifications for that and only then could they apply for Swiss citizenship. The same would apply for you if you want to get Swiss citizenship.