You can't do the equivalent of geosynchronous orbit around the Moon. If you compute the required distance, it lies beyond the Moon's Hill Sphere, and therefore it is not stable.<br /><br />L4 and L5 will only work with a little station keeping. They're not stable in the long term as there is too much eccentricity in the Moon's orbit and too strong of a solar tide through the Earth/Moon system. It's hard to keep exactly 60 degrees ahead of or 60 degrees behind something that keeps speeding up and slowing down. But a satellite carefully positioned can last several years without stationkeeping burns before it is expelled from its chaotic journey around the L4 or L5 point.<br /><br />But in L4 and L5, you would be the same distance from the Moon as you are when you are on Earth. And Earth is "sort of geostationary" to the Moon, hovering above its near side. A triangle of communication devices, one on Earth, one in L4 and one in L5 should allow you to cover almost all of the Lunar surface, but each station would be 1 Earth/Moon distance from the Moon.