A search for information on the Liberia token itself did turn up an extensive article by Randy Snyder in the September 2006 issue of Penny-Wise, the official publication of early American Coppers, Inc., but it had nothing to say about who struck the pieces

You skimmed over this article too fast. See p. 208; Snyder mentions three possibilities, and John Gibbs and Co. is obviously the correct one. Snyder says that they were actually made for circulation in the United States, not Liberia; the U.S. Mint would never have gone along with that, and importing them from England makes little sense since there was a suitable maker in New Jersey.

Josef Neumann wrote about the 1833 copper cent of Liberia in his seven volume work on copper coins written in 1863 (v. III p119-20 21277). After a description of the token and a brief history of the Colony, a reference is given to Blätter für Münzkunde 1835. 1 Band. Blatt 16 which states in German: 'Diese Münze ist geschlagen in dem Dorfe Belleville, 7 Meilen von Neu York in Nordamerika, wo bedeutende Kupfer, serbergwerke und kupserwaarenfabriken sind.'

In English: 'This coin is struck in the Belleville village, 7 miles from New York in North America, where there are significant copper mine and copper goods factories.'

A search turns up a Belleville in New Jersey, just across the river from Manhattan. The mine was known as the Belleville mine at one time. The relevant article with a fascinating history is found on Wikipedia.