Heat oven to 400ºF. Grease the bottoms of 12 muffin cups.
In a mixing bowl, combine the coconut milk and oats. Stir well, then let rest 5 minutes. Mix in the sugar, oil, vanilla, and eggs.
In a second mixing bowl, combine the flour, baking powder, baking soda, and salt.
Stir the wet ingredients into the dry ingredients until just combined, being careful not to overmix. Stir in the blackberries.
To make the filling, combine the cream cheese, lemon zest, and sugar. Stir until smooth.
Fill each muffin cup about halfway (there will be some batter left over). Spoon 1 scant teaspoon of filling into the center of each muffin, pressing it down into the batter. Top with remaining batter, covering the cream cheese filling completely.
Bake 15-18 minutes, or until the tops are golden brown and spring back gently when you touch them. Remove from oven and let cool completely before removing from the pan.