How do you best handle a customer who wants a refund because they "didn't find product as valuable" as they thought it would be?

Find the root cause. If the fault is within, refund. If it is by the customer, politely insist on paying. (you can take a call on a certain discount factor in a50-50 cases). You cannot demotivate staff accepting blame for mistake not done by them and penalizing them.

First we need to understand the customer and listen to him very carefuly so that we can conveince him regarding the problem faced by him .and we can suggest similar product to fullfil his requirement.

Ill understand the reasons and based on it ill try to come to level with him and the incnvience

i might give another items which works better

or give a gift away

then if i fail to please him ill refund just to win him back

First of all, not sure what you have in your agreement about refund. Just2 months into their annual contract, I think you are better off refunding (prorated of course), rather than risk a PR (if not legal) issue for you. In a way you are experiencing what many Premium vendors go through.If I were you I would use this as an opportunity to learn from them on what caused the value-prop gap. Conceivably your sales team/marketing convinced them of the value your product delivers and they bought into it (no pun intended). Seems like this is a good opportunity for your customer success/engagement team to tighten up their process. It should not have taken two months and for the customer to figure out that they don't value the product as much as they did when they signed the agreement. Your team should have seen the signs and jumped in to help them along. Treat a new customer in their early days like you would treat your toddler just beginning to walk. They might fall anytime. So have harnesses and be ready to help. Track and Analyze their usage and offer up help. There are many tools out there to help with this. One customer saved from abandoning your product,otherwise this is a good question.

It really depends on the company's rule and policy. Me, as a customer service representative, should apologize for the fact that we were not able to meet his/her satisfaction but the action depends on the higher team. They may give the refund, change the product or just ask for an apology. And my task is to explain it well to the customer. 

The customer is always right

Give him a credit note to spend at your store only

The best Handel the kind of situation I will show the about refund policy

Find the fault with the product, if it's the company's fault I'll try convince the customer to a different product and if they insists on a refund I'll refund to make them feel contented and retain them

pacify first the customer, by inviting him/her to a comfortable office area- listen carefully to the needs or concern enable to determine the issue.

As needed, introduce and encourage any alternatives of the product.

first i would try to understand the need of the customer based on that i would try to convince 

We need to understand the bottom of the problem and see & analysis what is the cause for it. If the mistake is ours we should immediately accept the product back and refund the money but if the customer is responsible and the product is exactly the same as it was when the customer purchased it. We must apologize and say to the customer that we regret to inform him/her that we have a no refund policy however we are really sorry for any inconvenience caused to the client and we can compensate for it by offering him some discount coupons for the customer's next purchase.