It sounds like you are describing rings composed of material with a low albedo. That is, material that doesn't reflect very much light. In this case, your rings would not affect the planet any differently that regular rings made of ice dust or moon-lets. In fact, that second material may be a bigger concern. Planetary rings are not flat. They could contain objects that are big enough to have significant gravitational mass. Not significant enough to cause major issues, but can actually help define the edge of the rings for a crisp line.
As long as your rings are not composed of dense material or densely populated by space rocks (and it doesn't sound like your rings would be if they are basically like a really cloudy day), you should be fine. If that slight mass of the objects that make up your rings is evenly distributed around the planet, you should not have to worry about tidal forces or anything like that.
In fact, unless your planet has a moon (or two or three or more), the tides on your planet will only be caused by the star the planet orbits. That means your planet's tides will be more or less proportionate to how far away the star is and how big it is.
The wikipedia page for ring systems briefly mentions some math that can help determine what kind of rings your planet can support, based on mass and volume and orbital height. https://en.wikipedia.org/wiki/Ring_system
Probably not necessary unless you are going for The Martian level detail and scientific accuracy.