Thank you for taking the time. I have an email in progress but the answer is below. Things would be more simple if the web page I viewed included those three key words: per calendar year.

Even this one, http://www.embassyofjamaica.org/visitors/general_information_visitors.htm
says "In general, non Jamaican nationals are landed as visitors for varying periods up to six (6) months." with no mention of per year.

However, in:
http://www.embassyofjamaica.org/VISnorthamericanvisitors.htm

the important item is what you said Lola, in the fine print:

Travellers are also advised that the period of stay is granted at the discretion of the Jamaican Immigration authorities. Frequent travellers to Jamaica should note that note once the cumulative number of days landed, exceeds 180 days in a calendar year, they are required to obtain a visa from the nearest Jamaican consular mission or post, prior to being re-admitted into Jamaica.

So that is the official answer.

After finding it, I used the search routine on the same site for "per calendar year"
and got zero results. Go figure. Yet the same string on

http://www.congenjamaica-ny.org/?s=per+calendar+year

does give a result which is below but would not have answered the question I posed.

----quote-----
Foreign and Commonwealth nationals entering the country to conduct short-term business, such as consultations, meetings, inspections, repairs, technical advice, are admissible as visitors, in accordance with the entry requirements applicable to visitors from their respective countries.

Each visit should not exceed thirty (30) days and the cumulative number of days within a calendar year should not exceed one hundred and eighty (180) days.

Persons travelling to Jamaica on business must be in possession of the following documents:

valid passport
return or round trip ticket;
a visa, if applicable
===end quote========

One ironic item is that at another time, on another official site, their internal search routine found a document which everyone else was saying did not exist