Hi Ashish, Konkan constitutes of a very big area in three different states i.e. Maharashtra, Goa and Karnataka. you can do a trip of Konkan region in 7 days but it would depend upon the destination you are covering in this journey and how are you travelling. If you are travelling in your own vehicle you can cover maximum destinations. Travelling in public transportation will limit your options. I'm sending with this comment few posts that can help you plan your trip.
Konkan region is really vast, and it had a lot to offer. So, covering the entire area will become messy. It's better to just pick some location and enjoy that.
Konkan is a beautiful place to enjoy with friends and family. It is a relaxing holiday. So if you plan it accordingly then I hope you will manage it in a week.