At American Creation Brian Tubbs accurately notes John Adams' call to prayer as President. He also notes the ironic dynamic that the prayer sounded Trinitarian but Adams himself was a unitarian.
It should also be noted that Adams regretted that call to prayer and claims that it cost him the Presidency against Jefferson.
As Adams explained, the prayer made him and America sound more "orthodox," less religiously pluralistic than they really were. As he noted:
The National Fast, recommended by me turned me out of office. It was connected with the general assembly of the Presbyterian Church, which I had no concern in. That assembly has allarmed and alienated Quakers, Anabaptists, Mennonists, Moravians, Swedenborgians, Methodists, Catholicks, protestant Episcopalians, Arians, Socinians, Armenians, & & &, Atheists and Deists might be added. A general Suspicon prevailed that the Presbyterian Church was ambitious and aimed at an Establishment of a National Church. I was represented as a Presbyterian and at the head of this political and ecclesiastical Project. The secret whisper ran through them “Let us have Jefferson, Madison, Burr, any body, whether they be Philosophers, Deists, or even Atheists, rather than a Presbyterian President.” This principle is at the bottom of the unpopularity of national Fasts and Thanksgivings. Nothing is more dreaded than the National Government meddling with Religion.
-- John Adams to Benjamin Rush, June 12, 1812. Old Family Letters, 392-93; taken from Hutson’s The Founders on Religion, 101-02.