Coconut oil, olive oil and butter or clarified butter are delicious fats that are also healthy for you, but the real original Paleo fats are animal fats.
I know that a lot of people following a Paleo diet end up consuming those fats only very rarely partly because they are harder to find, but also because more work needs to be done with them to obtain a pure fat to cook with. In other words, they need to be rendered.
The advantage of animal fats like tallow, lard or poultry fat is that they contain fat soluable vitamins A, D, E and K, nutrients and essential amino acids that cannot be sourced from not meat or dairy sources. Source fats only from well managed organic stock that has been grass-fed and pastured.