The idea 'covenant' is rather foreign. At least it is not an idea we often used to refer to the relationship we have with fellow Christians. We use the term to refer to promises God has with his people, that God has made a covenant with his people and he would keep it as he is faithful. But when it comes to link Christians within a group as having a covenant with each other, it shed a very different beam of light to the relationship that we have.
A covenant is more than a contract.
A covenant is more than a service-providing agreement in the commercial sense. Rather, it is a vow of promise to keep. It is a self-initiative bond that one enters into with a chosen person of persons. It resembles the Biblical understanding of the term that we are first of all chosen by God to enter into an organic relationship with the church. (Note that the Biblical understanding of the 'church' is not a physical construct, not a program that we attend, nor is it a certain leadership. It is the organic group of people whom God has chosen for himself to fill with His Spirit, both contemporary, historical as well as those who would come in the future.)
A covenant is therefore, a free and willful agreement that one makes towards the members of a group with a set of promises. The church is by nature a covenant group in the sense that its members have entered into a covenant with God who has chosen them. This covenant includes as its resulting part a covenant amongst and between its members that they should carry out the commandments of Christ that they should love each other and bear witnesses to Christ. Being a Christian, being a disciple is not a lone and individual journey.
Covenant should be a qualifying word that distinguish a church from the rest of human groups.
