I'd say it is possible given the right circumstances and a slight modification to earth...though it might not be stable over a long period of time (decades).
The best pattern I can think of that would account for that is what occurs to the Pacific west coast. There is a weather pattern known as the 'Pineapple Express' that is driven by trade winds. Essentially the equatorial ocean waters receive a very constant heat (near Hawaii in this case) that creates a steady stream of clouds (can be referred to as an atmospheric river). These clouds are caught up in the trade winds and sent a bit northward as it travels towards land and eventually dumps it's rain all over Seattle and Vancouver. In winter months, Vancouver is well known for entire months of clouds and rainfall (from heavy rain, to a light misting) with people never seeing the sun. The grey blahs as we will. The seasons change here though and the trade winds shift north and south as different parts of the globe are heated.
On an earth-like planet that lacks the seasons (IE, less of a tilt), these trade winds could become essentially static, allowing for this pattern to maintain itself for an extremely long period of time. Climate change here on earth seems to be making these trade winds more prominent as is...more energy in the system appears to be making these trade winds stronger.
So add a few degrees to the world and lose the seasons...and I think you can have the effect you'd want here.
Not all too sure on man-made...storm seeding is a potential, but you require the clouds to do so. Sometimes the conditions just aren't right for rain to form..the water needs something to form around or it remains a gas. Storm ceding in this case would be delivering silver iodide to the clouds. These particles act as nuclei for water particles to gather around, form water droplets, and then fall as rain.