I have a slim body (5'9", 64kg) and I would like to gain some weight (~72kg) in a healthy way (not by adding fat) I don't want to do any kind of weight lifting, push-ups or pull-up.
Is this possible?
Its most probably not possible, at least not to an extent that would make a noticeable difference.
While a change in diet is necessary to provide enough protein, you need some kind of stimulus for the muscles to grow, altering your metabolism and hormone balance to enter muscle hypertrophy.
Please take note, that typical low intensity activities are not enough, high intensity and preferably resistance trainign are a must. Compare the body composition of a marathon runner and a 100m sprinter.
Besides diet and exercise there are other factors, but none of them is substantial without exercise. If you want to know more about how to gain muscle mass, there are other questions about it.
You can make use of appetite tablets like Vitamin B, I am sure if your appetite improves you will eat more but you should watch what you eat. It has to be healthy foods with all necessary nutrients that help build up your body. You can also try dietary supplements, some will definitely help you gain weight.