Moss and it's close cousin, algae are very persistent (since they are one of the oldest life forms on Earth)... but yours is probably a moss rather than algae, since algae normally propagates in water.
Regardless, there are anumber of products that will kill either. Here in the U.S. an environmentally friendly brand of such is "Safer". It's simply sprayed on the infected area. It may take two or three applications, but it does work.
You're right... if the sun were able to penetrate the area, you wouldn't have such a problem. Failing that remedy, simply washing the area in a bleach/water solution every month or so(following the Safer application) will take care of it once it's eradicated... Be sure to use oxygen bleach (about a cup to a gallon pail of warmish water) and be sure to keep the solution wet on the area for at least fifteen minutes.
If the "yard" is paving blocks, concrete or even wood, you could use a sealer (here in the U.S. there are a number of all surface clear sealers like this:
http://www.hytechsales.com/clearcoatings.html )...