It is obvious why the word "centurion" does not appear in the Old Testament. The last book in the O.T. was written around 400 B.C. and the Roman Empire was yet future. To the best of my knowledge, no other army had centurions. The word appears only in the Synoptic Gospels and Acts of the New Testament. John does not mention the Roman leader of one hundred soldiers in his Gospel or his letters.
Matthew speaks of two instances regarding centurions. In 8:10, "Jesus marveled, and said to them that followed, 'Verily I say to unto you, I have not found so great (a) faith, no, not in Israel.'" Later in Matthew 27:54, the centurion at the crucifixion of Jesus said, "Truly, this was the Son of God." Most scholars believe Matthew wrote his Gospel to the Hebrews. For him to paint a gentile soldier in a good light is amazing. Luke speaks of the same two instances in 7:9, and 23:47, but he tells us something extraordinary. The centurion "glorified God, saying, 'Certainly this was a righteous man.'" Speaking of faith, wow! Mark speaks only of the crucifixion scene, and his quote is the same as that of Matthew.
The book of Acts, also written by Luke, presents centurions in a very favorable light. In 10:1-48, Cornelius, a Roman centurion was the first Gentile to believe the Gospel and be accepted as a member of the Body of Christ. In 22:26, it is a centurion that listens to Paul, and stops Paul's scourging. In 23:17, another listens to Paul, and does what Paul asks. In 27:3, Julius, a centurion, treated Paul in a courteous manner. It took a storm and severe hunger for the centurion in Acts 27:9-44 to listen, and even protect Paul from the soldiers. Apparently, the centurion rewarded Paul for his counsel by allowing him to stay a week with friends, and later, to have his own private "cell" where many of his friends could visit him (Acts 28:11-16; and several of his epistles or letters).
The reason, I believe, that the Bible reveals the positive actions of centurions during the early years of the Church, is because most of the readers were Hebrews, and as such, needed to lose "their attitude" against Gentiles. These passages clearly "messed with" the prejudice that must have been characteristic of the early Church. Maybe there is a lesson for us, in that, if God could use Roman soldiers to bless believers, it is very likely that members of other races, nationalities, religions, and yes, even political parties can be used of God to further His agenda. After all, God is no respecter of persons, so why are we?