https://jutakingstonchapter.com/tours.php?type=2
Kingston is not a big tourist destination but I find JUTA is way more organized there than in MoBay or Negril. I have stepped off the plane in Kingston, gone to the JUTA desk and they have a driver waiting right there. The manager asked where I was going, he looks in a book and says it will coast this much to go to that hotel. I also found the fare to be quite reasonable. The web page above has a list of tours so try messaging them and see what kind of vibe you get from talking to them.
I have phone numbers for 2 drivers that have picked me up but try the JUTA Office first.