Question: We are a small team of developers making and maintaining a software product with a high number of users. 

We are also in direct contact with users who ask us many requests about the product. 

We don't have access to business information (what kind of deal a specific user has with the company that employs us). 

We don't have enough resources to address all the user requests, and will have to refuse some of them. We treat in priority the requests that seem easier to comply with ; or that could benefit most users. 

How can we gracefully notify those users who made requests that we will not be able to process?  

How to tell them that what they asked for is not possible ; while avoiding frustrating them?

Answer: 
> 
> We don't have access to business information (what kind of deal a
>  specific user has with the company that employs us).
> 
> 
> 

This is the key thing. Unless you know the contractual details of a customer you can't make a decision as to how to reposed to a customers request.

The obvious thing is boot the request further up your managerial tree until it hits someone who can make that decision for you. 

In fact all change requests should be filtered through someone who is aware of the contractual requirements before you even start to work on them. As while you may think that an item seems reasonable, it may be totally out of the scope of what your customer has paid for, and by working on it you are effectively giving away free work.
Pass information up, and receive decisions that come down.

You should record all the client requests in an issue tracking system, but place them into the backlog (so they aren't worked on). The project manager (you should have one, of some sort, I hope) will review the requests on a regular basis, and decide which ones should be worked on. That PM is the person who should have the business and contractual knowledge (from the client) and techncial knowledge (from the request) in order to prioritize the work. 

Once you have that type of workflow in place, you never have to say no to a client - you always say that you'll ticket it, and Ms XYZ will prioritize it.