An excellent selection of how different theologians have defined the term ‘covenant’ is available here: https://www.gracecommunity-pca.org/podcasts/SundaySchool/Covenant/Definitions_of_Covenant.pdf
For those that have lost children in infancy, it can be a rather difficult journey to work through the grief. Yet Christian parents find their ultimate hope in Christ. The Synod of Dordt (1618-1619) wrote concerning the salvation of the infants of believers in Article 17:
The Salvation of the Infants of Believers
FIRST HEAD: ARTICLE 17. Since we are to judge of the will of God from His Word, which testifies that the children of believers are holy, not by nature, but in virtue of the covenant of grace, in which they together with the parents are comprehended, godly parents ought not to doubt the election and salvation of their children whom it pleases God to call out of this life in their infancy (Gen 17:7; Acts 2:39; 1 Cor 7:14).
An essay titled A Promise for Parents: Dordt’s Perspective on Covenant and Election by W. Robert Godfrey was recently published in Church and School in Early Modern Protestantism: Studies in Honor of Richard A. Muller on the Maturation of a Theological Tradition, Edited by Jordan J. Ballor, David S. Sytsma and Jason Zuidema. This entry has particularly helpful quotes intended to strengthen the confidence in the grace of God that believer’s children dying in infancy are in heaven.
Various delegations to the Synod expressed their views on doctrinal matters that are published in the Acta Synodi Nationalis…Dordrechti habitae Anno MDCXIX (Dordrecht, 1620), that gave shape to the final articles of the Synod of Dordt. Along with selective quotes from the Acta, Dr. Godfrey provides John Calvin quotes to show Calvin’s views influenced the delegates to the Synod. Christian parents should find great consolation because of God’s gracious covenant to His people and their covenant children.
Below are a few selections with the hope that others will find comfort:
The Bremen delegation stated:
We determine about the children of believers only that those who die before the age of doctrinal understanding are loved by God and are saved by the same good pleasure of God on account of Christ, through Christ, and in Christ as the adult: therefore they are holy from the relation of the covenant, the reality of which is confirmed by grace when they are initiated by sacred baptism and put on Christ.
pp. 379-380 (Acta, 2:63)
The delegation of Dutch professors wrote:
There is a great difference between those infants born to parents in the covenant and those not born in the covenant… we conclude that the children of believers dying in infancy ought to be reckoned elect since they are graciously taken away by God from this life before they have violated the conditions of the covenant. We are of the opinion that the children of unbelievers born outside the church of God, ought to be left to the judgment of God. For ‘those who are outside, God will judge,’ 1 Corinthians 5:13
pp. 379-380 (Acta, 3:10-11)
Professor Franciscus Gomarus wrote:
We piously believe that the infants of true believers, covenanted to God through Christ are also elect, if they die before the use of reason, from the formula of the covenant: I am your God and the God of your seed (Genesis 17 and Acts 2:39). But if they should attain to the use of reason, we recognize only those to be elect who believe in Christ, indeed according to the Gospel, only these are saved.
pp. 380-381 (Acta, 3:24)
Yet, (you say) there is danger lest he who is ill, if he die without baptism, be deprived of the grace regeneration. Not at all. God declares that he adopts our babies as his own before they are born, when he promises that he will be our God and the God of our descendants after us (Genesis 17:7). Their salvation is embraced in this word. No one will dare be so insolent toward God as to deny that his promise of itself suffices for its effect.
p. 383 (Calvin, Institutes, IV.xv.20)
Commenting on 1 Corinthians 7:14, Calvin wrote:
Therefore this passage is a noteworthy one, and based on the profoundest theology… the fact that the apostle ascribes a special privilege to the children of believers here has its source in the blessing of the covenant, by whose intervention the curse of nature is destroyed, and all those who were by nature unclean are consecrated to God by His grace.
p. 383 (John Calvin, Commentary on the First Epistle of Paul the Apostle to the Corinthians (Grand Rapids: Eerdmans, 1960), 149 on 1 Corinthians 7:14)
Church and School in Early Modern Protestantism: Studies in Honor of Richard A. Muller on the Maturation of a Theological Tradition, Edited by Jordan J. Ballor, David S. Sytsma and Jason Zuidema