Has the Church said anything against the enneagram?
Yes. The recently released Vatican document Jesus Christ the Bearer of the Water of Life states,
An adequate Christian discernment of New Age thought and practice cannot fail to recognize that, like second- and third-century gnosticism, it represents something of a compendium of positions that the Church has identified as heterodox. John Paul II warns with regard to the "return of ancient gnostic ideas under the guise of the so-called New Age: We cannot delude ourselves that this will lead toward a renewal of religion. It is only a new way of practicing gnosticism—that attitude of the spirit that, in the name of a profound knowledge of God, results in distorting his word and replacing it with purely human words. Gnosticism never completely abandoned the realm of Christianity. Instead, it has always existed side by side with Christianity, sometimes taking the shape of a philosophical movement, but more often assuming the characteristics of a religion or a para-religion in distinct, if not declared, conflict with all that is essentially Christian." An example of this can be seen in the enneagram, the nine-type tool for character analysis, which, when used as a means of spiritual growth, introduces an ambiguity in the doctrine and the life of the Christian faith. (emphasis added)