In many ways it's easier to nail down 'incredible' theology than 'credible' theology. A universal furore, such as the Roman Catholic church has experienced recently (see post below), is quite a good sign of incredibilism. But claims as to what constitutes credible theology will probably always generate an argument or two. For example, credible theology is not the reduction of theology to what we can experience indisputably and speak about perfectly rationally. The Resurrection of Christ, for example, cannot be experienced indisputably: if the initial experience of the disciples is disputed, how much more our own claims to experience the Presence of the Risen Christ.
Nevertheless it is worth pursuing a credible theology, not least because it responds to the instruction in 1 Peter 3:15, 'always being prepared to make a defense to anyone who asks you for a reason for the hope that is in you.' In turn, a credible theology lies at the heart of our participation in the mission of God. In that mission God announces joyful, good news to the world. Inherent in the message of the gospel is the supposition that the message is able to be understood, otherwise it is not 'news'. We have four gospels, not one, or, more accurately 'one gospel according to four different authors', I suggest, because the apostles and their communications team (i.e. Mark, Luke, etc) understood the need for a credible theology.
For a Roman audience, for example, Mark communicates differently to Matthew whose mind is focused on his Jewish audience. Intriguingly Luke also has a Roman audience in mind, yet feels that Mark can be extended and reshaped. (This difference could possibly be explained by thinking of a general Roman audience for Mark's Gospel and a leadership class audience for Luke's Gospel). John's audience is perhaps more difficult to confidently describe, but it does seem to be one with a strong awareness of Hellenistic philosophy, possibly combined with a distinctive Jewish theology.
Today we seem to misunderstand our audiences. What may be credible within the congregation is all too often incredible when simply repeated outside. We could take a leaf from the apostles' communication strategy.