I admit that I am no expert on genetics, so I am open to anyone correcting me. My understanding is that blue eyes are recessive and if both parents have blue eyes, the children will always have blue. If both parents have brown eyes, they could have a brown gene and a blue gene and the kids could end up with either. I'm not sure how green fits in. I have brown and my husband has blue, and one of our kids has green and the other has brown.
Before DNA testing was common, I believe they tested paternity with blood types. I have A+, and my husband has B+, and I've joked to him before that that is the one combination for which our children could have anything. So that blood test would be totally inconclusive.