Often, general books on composition offer projects as well as guidelines, but they take some searching out.
I have a book called The Simple Secret to Better Painting by Greg Albert. It is quite new, and probably available through Amazon. In it, there are pages which explore design ideas. "Design a Preference Test" "Play with Design" (exercises to do) "Another Design Game" (more imaginative choices) "Visual Tension" (a set of designs which show how something can be boring, while others have more tension, or even become distrubingly chaotic); "Visual energy" "Visual weight" "the dynamics of the frame".
From these ideas, you could develop your own projects, tho the book does go on to show lots of paintings, and explains WHY they work in terms of design and composition.
Another good book is "Drawing on the artist within" by Betty Edwards, who wrote Drawing On the Right Side of the Brain. Here is what it says on the flyleaf: "In a series of dramatically effective exercises, Betty E demonstrats how to stimulate and develop your capacity to think creatively and bring imagination and insight to the experiences of your everyday life You will discover a new awareness of your creative potential". So that one offers exercises too - see if you can find it in a library perhaps, to see if it is what you are after.
Or, Go to a shop which has lots of art instruction books for sale and have a browse through. You may well find what you want.