You can’t do everything. At times you get so bogged down with daily activities that it is simply impossible to take on another project. How can you say no diplomatically?
Sometimes you can’t. The project may have a high priority and have to be completed. Take a look at your other projects and see if any can be delegated or temporarily set aside. You may have some projects ahead of schedule and can afford to postpone them or some that are just not as important.
Talk with your boss to see if he/she has any suggestions on which projects can be postponed or delegated to someone else in the company.
Reschedule. The new project may not be a high-priority but one that can wait for a more appropriate time. Maybe the project can be done more effectively by another team member. Talk with your supervisor about the project, time constraints, and priorities for suggestions.
When you say no to an assignment, show how it will inhibit completion of higher priority projects and suggest alternate solutions.