If you build the parasol slightly sunward of the L1 point the parasol will not be in the correct orbit, so will drift off station. No matter what you do the shade will drift, so you will need some kind of station keeping.
I think that colouring the shade black won't help. as the momentum of the light is transferred whether the photons are reflected or absorbed. (please correct me if I am wrong).
My suggestion is to make the shield like a drogue parachute, with a counterweight on the sunward side; a system of controllable guy ropes and flaps would allow the drogue to maintain constant active control. This action could be powered by solar energy collected by the shade itself.
Alternately the parasol could be a swarm of inflatable spheres or disks each under active control, a nightmare to coordinate without using some sort of smart AI program.
This page I have made shows a sunshade created in Celestia (near the bottom of the page); Grant Hutchinson wrote the .ssc for this parasol, and I have used Runar Thorvaldsen's texture for a terraformed Venus.
http://www.orionsarm.com/worlds/Venus.html