Likewise, wives, be subject to your own husbands, so that even if some do not obey the word, they may be won without a word by the conduct of their wives, when they see your respectful and pure conduct. Do not let your adorning be external—the braiding of hair and the putting on of gold jewelry, or the clothing you wear— but let your adorning be the hidden person of the heart with the imperishable beauty of a gentle and quiet spirit, which in God's sight is very precious. For this is how the holy women who hoped in God used to adorn themselves, by submitting to their own husbands, as Sarah obeyed Abraham, calling him lord. And you are her children, if you do good and do not fear anything that is frightening. 1 Peter 3:1-6
If the unregenerate person is your child and the child lives in your home you will still be able to influence them daily. Your actions and demonstrations of faith will not return to you empty; no matter how deadpan and disinterested your child seems to be please know you are making an impact upon their hearts and minds. They will always remember your unconditional love and caring for them.
If your child no longer lives in your home you can still bless them by keeping in frequent contact with them. The wonders of internet, text messaging, social networking sites and webcams will allow you to be an influence in their lives to some degree. Just as with an unregenerate spouse you cannot whine or nag them into the Kingdom of God.
In all cases a very strong power you have is that of prayer. Pray for their regeneration and pray for their repentance. Pray that God would do whatever is necessary to accomplish His perfect and pleasing will in their lives.
And then, you live your life. This is part of accepting God's sovereignty in your life and in the life of your loved one. You will always love them, and hope always lives until they take their last breath.