I have some experience of teaching a course in Mathematics for libearal arts and social science students. It was called last year "the beauty of mathematics". Here is a blog post about the course, and the course page which contains all the presentation (in Hebrew).
The main topics of the course were
Numbers: irrational numbers, imaginary numbers, different representations of numbers, prime numbers and their properties.
Shapes: Geometry from two dimensions to many dimensions.
Infinity: The concept of infinity. The paradox of motion. How to add up infinitly many numbers.
Riddles: Mathematical puzzles and riddles.
Models: Mathematical models as the gate to science.
Probability: The mathematics of luck.
Games: mathematical games and the theory of games. Mathematics in social sciences.
Of course, there is much to be chosen from and it is quite important not to squeeze too much to a single course.