Don’t make the image darker. Instead try to make the image have more contrast. Use stronger key lights and weaker fill lights. The rule of thumb is that your ratio of intensity from key light to fill light should be between 16:1 and 6:1. Instead of leaving parts of the image black try to fill in dark areas with blue/purple lights.
For daylight lighting you want to have a low contrast. Your fill lights to key light ratio should be 1:4. The more cartoony you want to have your scene, the more evenly lit it should be with strong fill lights. Keep in mind if your light source is coming from inside or outside. If the scene were being recorded by a camera set for indoor lighting, then any outdoor lights should have a blue tint. If the camera is set for outdoor lighting then indoor lights will have an orange tint to them.
When starting to light a scene it is usually best to start with a 3 point lighting scheme and build from there. First thing I do is decide where the main light source is and place a light for that source. Then I add a fill light so the shadows aren’t black. Then I start looking at objects to see what might need a fill light. After I have the general set up I start adding lights as I want little changes to the overall look. You don’t necessarily need very many lights to do a great job.
Contact shadows help with the feeling of a scene a lot. Use negative lights and link them only to the object you want to create a shadow on. Or you can create negative lights with white shadows to add specific contact shadows.
Another thing to think about is what color you use on objects in the foreground vs. the background. Try to think about what colors will make things look like they are in front or in back (for example warm colored objects look like they are closer and cool objects look like they are in back. If you have a blue and red object at the same distance, the red will look closer and the blue will look farther away.) Also closer objects tend to be more saturated.
You might also want to think about if any wall or objects are reflecting any lights. In real life lights bounce off of everything around them. Lights also pick up color from the objects they bounce off of. For example say I am lighting a scene with a red wall and white floor. If the main(key) light is hitting the red wall. I might add a red spot light that points from the wall to the floor to simulate how that light would bounce in real life.
As you start adding lights it can get confusing exactly how every light in your scene is affecting the scene. You might think one light is doing something but its actually doing something else. There are two good ways to figure out what your lights are really doing. You can hide all of the lights in the scene except one and render. Then you will be able to see exactly what that one single light is doing. You could also check to see what a few lights are doing at a time by setting their colors to very different saturated colors.