Titus 1:6

if any man is blameless, the husband of one wife, having children that believe, who are not accused of riot or unruly.

This list of the qualifications of elders is substantially the same as that given to Timothy (1 Timothy 3:1ff); and that list with the comments should be noted in connection with what is written here.

Blameless ... means "above reproach," and is an inclusive term that appears to blanket the whole list of checkpoints enumerated.

Husband of one wife ... There can be no doubt that heads of families were alone considered suitable material from among whom the appointment of elders was to be made, as indicated by the entire context. The historical church sinned in the development of a government by celibate priests. This qualification does not allow an elder to be polygamous, nor to be divorced and remarried except upon Scriptural grounds.

Having children that believe ... Despite the fact that this is usually interpreted to mean "children that are baptized believers," that is not what the passage says. Of course, it could mean that, because Paul frequently used "believing" as a synecdoche embracing all of the primary steps of obedience to the gospel; but there is no certainty that he did so here. The opinion of Zerr is worthy of consideration:

My conclusion is that "faithful children" in Titus 1:6 is equivalent to controlled children in 1 Timothy 3:4,12, where the same point is under consideration, and hence that they are to believe in and be faithful to their father, regardless of whether they are members of the church or not, or even that they are old enough to be members.[18]

Who are not accused of riot or unruly ... This states the qualifications negatively, riotous, unruly and disobedient children in any man's family being enough to disqualify him.