Acts 8:37 is not included in many Bible translations because it is not found in the oldest and best translations of Acts. There is no attempt to cover it up, as you can find it (with an explanation) in the footnotes of most Bibles. In fact, the Catholic Douay-Rheims New Testament includes Acts 8:37: "And Philip said: If thou believest with all thy heart, thou mayest. And he answering, said: I believe that Jesus Christ is the Son of God."
The Haydock Bible Commentary explains the meaning of "If thou believes" in this way:
The Scripture many times mentions one disposition, when others no less necessary are supposed, as here a sorrow for sins, a firm hope, love of God . . . Faith is thus seen to be a necessary predisposition in the adult, for the reception of baptism. They must answer for themselves, but infants are baptized in the faith of the Church. Their sponsors, who receive them from the font, answer for them. And as the defilement was not personal, but that of others, so are they purified by the faith of others.
About Acts 8:37, The Navarre Bible Acts of the Apostles Texts and Commentaries
This verse, not to be found in some Greek codexes or in the better translations, was probably a gloss which later found its way into the text. In the Vulgate it is given in this way: " Dixit autem Philippus: ‘Si credis ex toto corde, licet.’ Et respondens ait: ‘Credo, Filium Dei esse Jesum Christum,’" which, translated, would be: "Philip said, ‘If you believe with all your heart, you may.’ And he replied, ‘I believe that Jesus Christ is the Son of God.’" This very ancient gloss, inspired by baptismal liturgy, helps to demonstrate that faith in Christ’s divine worship was the nucleus of the creed a person had to subscribe to in order to be baptized. On this occasion Philip, guided by the Holy Spirit, lays down no further condition and he immediately proceeds to baptize the Ethiopian. (105)
For more information, see "Misquoting Jesus vs. Misquoting Truth," at vivacatholic.wordpress.com.