What is the best way to tell an owner you no longer want to care for their dog because it isn't a good fit?

Honesty is the best policy, so tell the owner you aren't a good fit for their dog and provide them with valid reasons why you cannot provider further care. Since you are a new sitter as an FYI most dogs will act differently in your home than they do at their home, its just the way dogs are, so plan for the future. Best of luck