Wow, that’s tough. It really depends on many variables. If you really do not have the time or the resources then you need to let them know in a professional way. Use your Emotional Intelligence. In other words, don’t bite their head off. Instead, empathize with them and explain why you cannot handle the request at that time. Keep in mind, they are your client, so pick your battles wisely. You want to service that customer but don’t over promise if you cannot handle the request.
What is worse? Promising and not delivering or owning up to it, say no, and keep your client happy. If you have the habit of not being able to say no, you may have some adjusting to do.