I do not believe 1 Timothy 3:4 and Titus 1:6 require a man who would serve as an elder to have a plurality of children. In other words, I believe a man with one child is Scripturally qualified to serve as an elder, if he meets all the other requirements.
“Offspring” Vs. “Children”
1 Timothy 3:4 says, “one who rules his own house well, having his children in submission with all reverence” (NKJV). Titus 1:6b says, “having faithful children not accused of dissipation or insubordination” (NKJV). What does “children” in both these passages mean. The Greek word in both scriptures is telknon, and its primary meaning is “offspring,” according to Thayer and others. Whether the “offspring” is one, or more than one, is not the point. Therefore, the requirement is that the man being considered for an elder must have offspring, i.e., one or more children. We must remember that “children” is the English word choice of the translators. It is a mistake, then, to make one’s argument on the singular or plural meaning of the English word “children,” and this is true for a variety of reasons.
Arguments Based On Webster’s Definition Of “Children” Just Don’t Cut It
First, Webster tells us that “children” is plural, but when he does so, he is not telling us the meaning of the Greek telknon. You’ll need to look up “offspring” for that definition. When you do so, he will tell you it is “the progeny of an animal or plant.” So, the man being considered as an elder is not required to have a plurality of children; instead, the requirement is “offspring,” whether one or more. Second, even our usage of the plural children isn’t consistent. For example, if we go to a restaurant that has a sign that says “children eat free,” we and the restaurant owner are not going to exclude our family from this deal if we only have one child. Third, and just for the sake of argument/clarification, let’s suppose that the Holy Spirit had used the singular “child,” would this have not eliminated every man who had more than one child from serving as an elder? Thus, we see just how unhelpful arguments based on the English word “children” vs. “child” can be, particularly as the Holy Spirit used neither of these expressions. Instead, He used precisely the right word to convey His meaning, for the Greek word He used is equivalent to the English “offspring,” which means a man’s progeny, which can be one or more. So, if we’re going to call Bible things by Bible names, then we must agree that a man who has offspring (i.e., one or more children) is qualified to serve as an elder, if he in turn meets all the other requirements. If not, why not?
It Is God, Not Us, Who Set The Qualifications
To raise an objection to a man serving as an elder because he has only one child is a very serious thing, particularly when the Holy Spirit did not use either “child” or “children.” Instead, He used telknon, which means “offspring” or “progeny.” Thus, He used a term that included both the singular “child” and the plural “children.” Remember, then, that it is God, not us, who sets the qualifications for elders. Our job is to do everything we can not to add to or take away from what God has said about this in His word. And let us all remember that it is just as wrong to bind where God hasn’t bound, as it is to loose where He hasn’t loosed.
 There are 99 occurrences of telknon in the New Testament. It is translated “children” 70 times, “son” 15 times, “sons” 6 times, “child” 5 times, “children’s” 2 times, and “daughters” 1 time. The all-inclusiveness of telknon is demonstrated many places in the Scriptures. Sometimes it is translated “child,” sometimes “children.” Sometimes it is even used both ways in the same verse. For example, in Matthew 10:21, Jesus said, “Now brother will deliver up brother to death, and a father his child [telknon]; and children [telknon] will rise up against parents and cause these to be put to death.” So, to put one’s emphasis on the meaning of the English translation of the plural “children” for the Greek telknon, which is “offspring,” and then argue as if this is what the Holy Spirit meant, is just not Scripturally sound. Incidentally, and I just couldn’t resist this, the subtitle of this section is called “Notes” (plural), although there is only one “note” (singular) in this section. Is this a mistake, or am I following convention (i.e, the MLA style-sheet) in doing so? I’ll let you be the judge.