Herbert Lockyer has published a book, All the Prayers of the Bible. The Table of Contents is an extremely helpful resource as you study prayer, for example:
Genesis
- Prayer History Begins Gen 4:26
- Prayer and Spiritual Progress Gen 5:21-24
- Prayer and the Altar Gen 12, 13
- Prayer for an Heir Gen 15
- Prayer—the Language of a Cry Gen 16
- Prayer and Revelation Gen 17
- Prayer for a Wicked City Gen 18, 19
- Prayer after a Lapse Gen 20
- Prayer of Obedience Gen 22
- Prayer for a Bride Gen 24
- Prayer for a Barren Wife Gen 25:19-23
- Prayer Changes Things Gen 26
- Prayer as a Vow, Gen 28
- Prayer about a Wronged Brother Gen 32
- Prayer—The Motion of a Hidden Fire Gen 39-41; 45:5-8; 50:20, 24
- Prayer for Blessing upon the Tribes Gen 48, 49
In his introduction to the Prayers in the New Testament (available at Google Books free preview), he writes on the differences between Old Testament and New Testament prayers:
As we approach the still richer treasure of prayer the New Testament contains, what else can we say but, “Lord, it is good for us to be here”? At the outset of our meditation, let it be clearly understood that while we find further confirmation, we do not have any higher evidence than the Old Testament presents of the fact that God hears and answers prayer.
From Genesis to Malachi we have ample proof of prayer being fully answered by God. No sincere saint was sent away empty. No petition in submission to the divine will failed of an appropriate answer. As the Bible, however, contains a progressive revelation of the mind and will of God, we have aspects concerning the duty and privilege of prayer of new and intense interest….
Prayers of the two Testaments are different in several ways. First of all, Old Testament saints were taken up in the majority of cases, with secular or temporal blessings. Their prayers were, more or less, of an earthly nature. One exception is David, whose Psalm-prayers were of a heavenly nature. Spiritual communion was his desire as he panted after God (Psalm 42:1).
The New Testament abounds with directions to pray for and seek after spiritual blessings (Ephesians 1:3). Under grace, believers are on vantage-ground. Theirs is a fuller revelation than that enjoyed by saints of old. They have been given specific directions on how to desire spiritual gifts and graces, with promises and assurances inspiring confidence to possess their possessions.
Herbert Lockyer, All the Prayers of the Bible