In an office environment answering a customer with the response "I will work on your project in my spare time". I feel there is a more professional way to answer. Suggestions?
Using the phrase "when I get a moment" might be appropriate. It implies that the task will be completed, if not at that exact time:
"I will work on your project when I get a moment"
As suggested in the comments, I also think mentioning working it into your schedule is a tactful way of getting your message across:
"I will work on your project as my schedule permits"