Originally Posted by Don Gelles

I will kindly offer that the qualifications for an elder does require that his children to be baptized members of the Lord's Church.

The word used in Titus is πιστός (pistos) and it is used in many places as an adjective to refer to a substantive (noun) in the Greek. It is thus used for those who are part of the Lord's Church or Christians. Examples:

In 1 Timothy 4:12 the word πιστός is used an no one argues it is referring to Christians even though the word Christian is not used in the verse. πιστός is an adjective and is being used to describe a "state of being".

In 1 Timothy 6:2 the word πιστός is used and no one argues it is referring to being a Christian even though the verse does not use the word Christian in reference to the master. πιστός is used as an adjective to qualify the substantive which is "master".

Taken in it's context, the passage in Titus 1:6 would lead us to understand that πιστός is being used to qualify the substantive (children). In its context there is no reason for us to not accept pistos as having reference to "those who are Christians or members of the Lord's Church". To further support this as being correct, the word ἀσωτία (riot) carries the understanding of not being in a state of "unsavedness". Thus, taken as a whole we see that the context of Titus 1:4 has children that are "Christians" in mind.

Kindly,
Don