Answer: No. Once your child can file married filing jointly, you no longer can claim them – even if you support them 100% and they have no income.
But if your child has a dependent (your grandchild) that also lives with you and you support them, then you may claim the grandchild. This also should allow you to qualify for the child tax credit and education credits for the grandchild.
Like any good CPA, I need to add a disclaimer: Unfortunately, it is impossible to offer comprehensive tax info over the internet, no matter how well researched or written. And remember, I love my readers but having me bookmarked on your computer doesn’t make you a client: before relying on any information given on this site, contact a tax professional to discuss your particular situation.