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Firstly make your website attractive. Analysis other coupon websites and find what they are doing. After that, I would suggest you to advertise your site through social media like, facebook, twitter, Google+, linkedIn, pinterest, Instagram, and others. now instagram is more popular than others.
Making your website functionally attractive and keeping it relevant and up to the expectation ( maintaining the quality) will make any website successful. Go for a deep research...visit other such websites, evaluate their positives and drawbacks. This will help you being more aware and prepared. All the best!!