In the September, 1829, issue of The Congregational Magazine, a cranky correspondent complains about an innovation of which he does not approve:

To the Editors.— … Many of your friends were surprised and amused to read, in your number for June, of a minister being ‘installed’ over the Congregational Church in Belfast, and of an ‘installation prayer’ having been offered on the occasion. We are familiar with the terms as connected with the different orders of knighthood among the nobility, and some of the higher functionaries in the national hierarchy, but for introducing them to describe the ‘installation’ of an independent minister, there surely exists no authority, and I am desirous of preventing your valuable miscellany being appealed to as countenancing such an abuse of words…. Yours, &c., Verbum Sat.”

The Congregational Magazine was a publication aimed at Nonconformists in the Reformed tradition who used congregational polity. In terms of their polity (i.e., church governance), they would have been fairly close religious relatives to mid-nineteenth century British Unitarians.

This seems to imply that “installing” a minister was a new practice in the mid-nineteenth century, at least among U.K. nonconformist congregations. So when did Unitarians and Universalists in the United States start talking about “installing” ministers? A quickie online search turns up plenty of mid-nineteenth century installation sermons, but nothing earlier than that.