OK, this one still needs some refinement...but based on the first couple of trials, here's my new improved recipe.
1 can coconut milk or coconut cream (chilled)
1 can crushed pineapple
1/4 c sugar
6-10 ice cubes
Put the crushed pineapple (with it's juice) into the blender and pulverize it into oblivion. Well, at least blend until it's not chunky anymore (otherwise you'll have chunky smoothie, which is not very smooth...)
Shake coconut milk/cream (before opening can), and then add to blender, along with sugar and ice cubes. You don't need the sugar really, but my husband likes his smoothies pretty sweet. An alternative would be a little plain pineapple juice.
Blend until smooth!
(You can also toss in a banana for texture.)