Covenant theology and dispensationalism are both systems defined by men in an attempt to make sense out of the varied times and teachings of scripture. I am a dispensationalist and think it closest to Biblical truth. However, I recognize that even this system can become a hindrance to learning God's word if we exalt the system over the clear teachings of scripture.
Covenant theologians like to discount dispensationalism because of its so-called recent invention. However, covenant theology as a system is a direct fruit of the Reformation and is less than 500 years old. It develops from the idea that God's entire plan for this world proceeds from covenants He made before creation (or at the beginning of time). The covenant theologians state that there were three (or two) covenants. The three covenants are the covenant of works (by which Adam was given a chance to earn his salvation), the covenant of redemption (by which the Trinity determined their separate parts in redemption), and the covenant of grace (by which certain individuals were chosen to be the elect and to receive the gift of salvation).
As such, covenant theology is closely identified with the Calvinistic view of election and predestination. And, although there have been dissenters, it is usually closely identified with infant baptism, as this is the way that children are brought into a covenant relationship with God (not to be confused with eternal salvation). Further, these connections have always made covenant theologians prone to push for the union of church and state. That is, the state (or national government) should determine the state religion. It is true that Baptists who have been covenant theologians have rejected these later ideas, but it has often caused them to be rejected or discounted by other covenant theologians. Covenant theology and Baptist distinctives have always had a certain tension between them.
Another theme central to covenant theology is the idea that Israel was completely and finally rejected by God and that the church (by which they mean an invisible, universal church on earth) has taken over the promises given to Israel. However, this claim of the blessings promised to Israel requires these blessings to be spiritualized to a tremendous degree. This leads us to another pervasive practice of covenant theologians. They must and they do allegorize much of the teaching of the Old Testament. Their spiritualizing of vast quantities of Old Testament real estate is one their greatest conflicts with dispensationalists.
Whereas covenant theology centers on redemption, dispensationalism centers on the glory of God. This is not to say that either system rejects either purpose. However, dispensationalism declares that God in His wisdom deals with men according to different orders (sometimes called economies). Each dispensation deals with man under a different set of ground rules or circumstances. One put Adam and Eve in a perfect garden. Another gave the nation of Israel a special law through Moses. A future dispensation will see Jesus Christ on the earth as King during the kingdom age. In each dispensation, man fails and demonstrates his inability to save himself. However, God gets the glory and a remnant of mankind find the grace of God. The circumstances under which man finds himself changes at times throughout the centuries, but history is moving to the time when all things that God has started (a redeemed earthly race, a righteous earthly kingdom of Jews, and a redeemed heavenly race) will be fulfilled.