Which Is The Best And Reliable Online Medicine Shop In Kolkata?

Though I am not sure which of these services have operation in Kolkata, there are a few good options for you -

Sastasundar
This is one of the popular online medicine shop for the Kolkata region. There have been quite impressive reviews about the site. Their customer care service is deemed to be one of the best in the industry. The online shop offers a faster delivery. They also offer a 15 percent discount and free delivery if your order value exceeds Rs. 300.
You can get more info from http://www.sastasundar.com

Mera Medicine
This is yet another great option for buying medicines online. The delivery period is 2 to 4 days. Moreover they offer amazing discounts. These may range from up to 15 percent. There are also other benefits like Amazon Gift cards for 10 percent of your order value.
The official link is http://www.meramedicare.com.

Mad Morning
Mad morning offers up to 23 percent discount on the medicines. They do offer free delivery. There isn't any minimum order value needed for the same. The service also has a mobile app for ordering the medicines on the go. They do have service in Kolkata.
Visit http://madmorning.com for more information.

Netmeds
Netmeds is a certified medicines shop that operates online. The quality assurance team on the site is an authorised one. They offer faster deliveries. Netmeds also provides special cashback on select orders.
You can find more about it at http://www.netmeds.com

There are several other options as well. Some of the worthy mentions could be :medicaldeal.in, pharmeasy.in and www.1mg.com.

Do they have card on delivery option, and how fast they deliver medicine?

You will need to get in touch with the respective online portals for the exact terms and conditions. Most of the operators do support Cash On Delivery and other modes of online payment. The exact mode that you can avail will be dependent on the exact amount of your cart value.
As for delivery, almost all of them claim to provide you delivery in 2-3 days. For some items, they may offer one day delivery option as well.

Here are some of the shops that allow the cash on delivery and the ship to Kolkata.

Netmeds

This shop requires you to upload the prescription before you can checkout in the shopping cart. You can also choose to pay the cash on delivery in shop. But one issue with it is that it has to be above certain amount, in order for it to qualify for cash on delivery. Also shipping costs apply and no free shipping from what I have noticed.
You can check out the shop here : http://www.netmeds.com

MedPlus Mart

This is another shop that does the home delivery. It can accept card on online order and cash on offline order. It has free delivery option in Hyderabad but not in WB. So if you are in Kolkata then it will go like any other place. You also have to upload the prescription in the site. You can also do the store pickup option if you have store nearby. You can check out the shop here: https://www.medplusmart.com/

pharmeasy.in

This another shop that may apply in your case. They do shipping in Kolkata. They have the cash on delivery option but thee card option should be online only in such case. You have to upload the prescription and choose your delivery method. You can learn more about it here : .https://pharmeasy.in

There are some other options such as Apollo Pharmacy and few others but you may have to find out if they do allow card on COD option. Not many online services may agree to that part though.