How do you say no as an answer to a customer and/or clients? Bear in mind, you can not sound rude.

First of all, saying NO is not an answer a Client is ready to hear. So personally I would pay close attention to the client's every word because with listening done right it helps provide an insight on an alternative option that I could offer the client rather than saying NO. In all my years of experience this has worked 90% of the time the other 10% of the time that it has not worked is when I involve my superior who clears out everything thus still keep the client happy with never saying NO.

Always try to come up with an alternate option instead of saying no to the customer. If there is no alternate option then be polite and explain the customer that unfortunately you are helpless.

Your tone should be reflecting your helpful nature in helpless situation to say NO with no other option. That's all the customer needs. No one expects always YES but genuine NO. 

You say to the customer 'this is what. I can do for you'

Well, this is varies according to the options, alternatives, and empowerment the customer facing employee have, however you should well understand the denial mechanism based on the alternatives you have as a customer facing employee to avoid being in this hard situations.

But after all there are still some phrases as an alternative for NO to be said like:

- I can see how that would be useful, but i am afraid we don't have currently plans to do this"naming the issue"

- While there is currently no availability to do that"naming the issue", we do really appreciate you taking the time to let us know what you are looking for.

- Most of our improvements came from ideas like yours, and we do really appreciate your feedback as an opportunity for us to serve you better in the future.

You should focus on what you can do instead of what you can't do

First of all i will apologize to the customer and provide him/her an alternate option according to the requirement of the customer. 

But if i don't have any alternate option as per customer requirements i will update the customer in very polite manner and ask the customer for any other assistance. 

You should not say No rather show willingness to do what can be done instead use proper words like .i am afraid this can not be done how ever i can do this for you.

Give another options that is close to his/her preference. Still, introduce it effectively so he/she wont feel any unsatisfactory.

We are really sorry to say Mr. or Ms (name of the client) or Unfortunately Mr or Ms. (name of the client) .

and if we have other choices however we have another choices. with a flat tone.

If the situation still forces to say NO to the customer, First of all I should apologize the customer, then I will say " I am extremely sorry sir, I am unable to help you in this regard as per the company / government policy to provide you this kind of service, I will be really happy to help you , if you would require any other service from us"