Titus 1:6 if a man is blameless, the husband of one wife, having faithful children not accused of dissipation or insubordination (NKJ).
There is more than one meaning to the word “faithful” (pistis/pistos) and it must be the context which enlightens us as to which meaning is required. To me, the context is very clear. “Faithful” is further amplified or clarified by the added words, “not accused of dissipation or insubordination.”
Now, the broader context. What Paul sets down as the qualifications for elders in Crete (1:5) would surely not contradict what he sets down as qualifications for elders in Ephesus (1 Timothy 1:3; 3:1-7). What does Paul say about an elder’s children in 1 Timothy 3:4-7?
4 one who rules his own house well, having his children in submission with all reverence 5 (for if a man does not know how to rule his own house, how will he take care of the church of God?); 6 not a novice, lest being puffed up with pride he fall into the same condemnation as the devil. 7 Moreover he must have a good testimony among those who are outside, lest he fall into reproach and the snare of the devil (NJKV).
Paul says nothing here about “believing children” but about children who are well-disciplined and under control. He then goes on to point out that if an elder can’t lead his family in this way, he surely can’t lead a larger group - the church. I believe that these words mean the same thing as “faithful” does in Titus 1:6. An elder is not required to make each of his children a believer, but he is required to have his children under control.
Now, the theological issue. Since when can any person be held accountable for the conversion of another? We are, of course, responsible to share the Gospel, but we cannot compel anyone to believe. To require that an elder must have all believing children is to assume that he is responsible to save them. If he can save his own children, then can he not save all others? But we know that salvation is God’s work. There is none righteous, not even one. There is none who seeks God (Romans 3). If this is true, then only God can open the heart of an unbeliever. Eli and Samuel were rebuked for not disciplining their children, not for failing to bring them to faith. If the requirement is for an elder to have children who believe, then he must be able to convert them, and this simply is not so.
All of this leads me to conclude that an elder must have “faithful” children. Children who are not “out of control,” who are well-disciplined and reliable, demonstrating good leadership on the part of their father.