To describe two functions which are equal every 216 days and opposite every 108 days after being equal, you simply need two sinusoidal functions properly scaled and shifted.
Moon 1: $\sin({{1}\over{216}}\pi \times days)$
Moon 2: $\sin({{1}\over{216}}\pi \times days - \pi)$
Overlaid, the functions look like this (shifting sine by $-\pi$ is the same as −sine):

Starting at day zero, the moons are at the same point in the function, 108 days later they are the maximum distance apart, after another 108 days (216 total) they are back to being at the same point.
If as SJuan76 points out, you want to have more realistic orbital periods (non-identical, but still line up as requested) you can just use a multiple period, like this:
Moon 1: $\sin({{1}\over{216}}\pi \times days)$
Moon 2: $\sin({{1}\over{72}}\pi \times days)$
