William said:
By faith in the covenant of particular election knowing that whatsoever God does is right, not presuming their salvation but raising them as if they were the Lords. The other option is to raise them believing that they are heathen.
William,
I am not familiar with "the covenant of particular election". Could you explain what this is and where in the Scriptures it is taught?
Secondly, I do not see how you can say on the one hand that you aren't "presuming their salvation", which would mean you are presuming their non-salvation, but on the other hand you say parents should be "raising them as if they were the Lords".

I fail to see what the difference is between not presuming their salvation but presuming they are of the Lord. In my understanding, if one "belongs to the Lord", then they are of necessity saved. The unsaved don't "belong to the Lord" other than He is their sovereign Creator and Judge.
Thirdly, it would appear that you have some aversion to believing that children of believers are heathen. Why is that? Was not the entire population of the nation of Israel considered to be "covenant children"? The majority of Israel perished in unbelief as covenant children. Did not John the Baptist preach repentance toward God and faith in Christ to the covenant children of his day? Were not those who opposed the Lord Christ most vehemently covenant children? What does Paul say about the spiritual condition of everyone who is born into this world?
Ephesians 2:1-10 (ASV) "And you [did he make alive,] when ye were dead through your trespasses and sins, wherein ye once walked according to the course of this world, according to the prince of the powers of the air, of the spirit that now worketh in the sons of disobedience; among whom we also all once lived in the lust of our flesh, doing the desires of the flesh and of the mind, and were by nature children of wrath, even as the rest:-- but God, being rich in mercy, for his great love wherewith he loved us, even when we were dead through our trespasses, made us alive together with Christ (by grace have ye been saved), and raised us up with him, and made us to sit with him in the heavenly [places], in Christ Jesus: that in the ages to come he might show the exceeding riches of his grace in kindness toward us in Christ Jesus: for by grace have ye been saved through faith; and that not of yourselves, [it is] the gift of God; not of works, that no man should glory. For we are his workmanship, created in Christ Jesus for good works, which God afore prepared that we should walk in them."
I cannot but believe that Paul was making a statement about
everyone's natural condition; Jews and Gentiles alike and that this spiritually dead condition is inherited at conception. (cf. Rom 5:12-18) And, it seems clear to me that salvation is not something to be
presumed but is evidenced by repentance and faith, those being the fruit of regeneration; aka: being made alive.
Thus, again, it seems to me that ALL children are born spiritually dead, are under the wrath of God and need to hear the Gospel no less than any other "heathen" from the nature of the case since they are born "heathen". And one last point of interest, NPP/FV teaches
covenantal presumption too, i.e., those born into the covenant are
presumed to be of the Lord's until they openly repudiate Christ. So, I cannot accept what you have proposed as being a valid argument in regard to either how one is to deem covenant children nor in the manner in which they are to be raised. If nothing else, my experience, which is certainly not to carry any monumental weight compared to the teaching of God's inspired Word, but in my experience the vast majority of "covenant children" exhibit a more sinful behavior when apart from family and church; at the hockey rink, etc., than do many non-covenant children.

In His grace,