A geostationary satellite can only be placed above the equator, and therefore could create an eclipse only on and around the equator (assuming it has the right size). Not very useful to observe circumpolar stars, together with the major complication that the atmosphere around the equator is usually really humid and therefore lowers the quality of the observations.
To generate an eclipse the satellite should have at least the same angular size of the Sun, which is about 0.5 degree. The relation between dimension, distance and angular size are expressed according to the formula $\alpha=2 \cdot arctg$$D \over L$.
Considering that the geostationary orbit is at 35786 km above the surface of Earth, this gives us a transverse dimension for the satellite of at least 333 km.
A structure of that size could be built with something similar to a solar sail, a thin and opaque foil kept in position by a frame, and it would be a challenge to balance it against the pressure of the solar wind and solar light. Not even mentioning the need to repair it against any hole created by micrometeorites.
Last but not least, the Sun is not at the same azimuth around the year. I am not a pro in orbital mechanics, but I am pretty sure that there is no way to keep a satellite geostationary while chasing the Sun along its walk across the ecliptic around the year.
Summarizing, a geostationary satellite would not be feasible: too large for our current technology level and not able to chase the Sun year round. To quote what AlexP stated in a comment to the question:
A stationary eclipse requires an object which sits always on the line between the Sun and Earth. Such an object revolves around the Earth with a period of one year. The radius of an Earth orbit with a period of one year is exactly the same as the radius of the orbit of the Earth; the problem is that there already is another object there, namely, the Sun