Trinity Church practices paedocommunion. Baptized children are members of the covenant and when old enough to partake of solid food they should be served the covenant meal (communion) as well. Tim Gallant has summarized the case for paedocommunion in the conclusion of his book, Feed My Lambs:
Let us briefly consider some of the ground we have covered. First, biblical principles lead us to include children in the sacrament of Lord’s Supper. It a sacrament for the body of Christ (1 Cor. 10:16-17; cf. 1:9), of which covenant children are a part (cf. 1 Cor. 7:14; 10:1-4); it is a sacrament which signifies and seals participation in His body and blood (Jn. 6:53), of which they do indeed participate (Mt. 19:13-14). It is a new covenant rite – a covenant which proclaims an equal share for all members in its benefits (Gal. 3:27-29; note that membership is specifically defined there as predicated upon baptism). If our children are members of Christ’s holy nation, they are also members of His royal priesthood (1 Pet. 2:9), and receive the full blessings of Christ’s altar.
Moreover, the Lord’s Supper draws a great deal of its character from Passover and other Old Testament sacraments (e.g. peace meals), in which children were participants. This was despite the fact that those sacraments, too, presented the possibility of profanation and included requirements of remembrance and appropriate manner of approach to the living God. Therefore, similar requirements in the New Testament in connection with the Lord’s Supper (1 Cor. 11) cannot validly be used as a prohibition against the participation of covenant children.
– Tim Gallant, Feed My Lambs: Why the Lord’s Table Should Be Restored to Covenant Children, Pactum Reformanda Publishing, 2002
Other books dealing with this topic include The Case for Covenant Communion (Ed. Gregg Strawbridge, Athanasius Press), and Given for You, by Keith A. Mathison.