Hi Anuj -
I think you are operating from a very false assumption that is going to hurt your organic traffic (I suspect it has already).
The XML sitemap is one of the the very best ways to tell the search engines about new content on your website. Therefore, by not putting your new coupons in the sitemap, you are not giving the search engines one of the strongest signals possible that new content is there.
Of course, you have to automate your sitemap and have it update as often as possible. Depending on the size of your site and therefore the processing time, you could do it hourly, every 4 hours, something like that. If you need recommendations for automated sitemap tools, let me know. I should also point out that you should put the frequency that the URLs are updated (you should keep static URLs for even your coupons if possible). This will be a big win for you.
Finally, if you want to make sure your static pages are always indexed, or want to keep an eye on different types of coupons, you can create separate sitemaps under your main sitemap.xml and segment by type. So static-pages-sitemap.xml, type-1-sitemap.xml, etc. This way you can monitor indexation by type.
Hope this helps! Let me know if you need an audit or something like that. Sounds like there are some easy wins!
John