Preheat the oven to 375 degrees F (190 degrees C). Grease cookie sheets or line with parchment paper.
In a large bowl, cream together the butter and brown sugar until smooth. Beat in the eggs one at a time, mixing well after each. Combine the flour, baking powder and salt; stir into the sugar mixture. Mix in pineapple and butterscotch chips. Drop cookies by rounded teaspoonfuls 2 inches apart onto the prepared cookie sheets.
Bake for 10 to 12 minutes in the preheated oven, or until golden. Allow cookies to cool on the baking sheet for 1 minute before removing to wire racks to cool completely.