My reply is too late, but for version 14, you must buy a COD from the store, or you can implement a Cash on Delivery method from the Payment Acquirers by following the steps:

1. Website Settings
2. Payment Acquirers
3. Create
4. Fill out the forum with your Cash on Delivery settings.
5. Select the right payment journal (important).

Now you have a COD option on your website without buying extra addons.

Enabling Settings > Website > Shipping > On Site Payments & Picking does this I think.

Did you check these modules:

- https://www.odoo.com/apps/modules/8.0/payment_cash_on_delivery/

- https://apps.odoo.com/apps/modules/10.0/website_sale_checkout_store/

Is there a free solution?

Hi,

You can see http://www.probuse.com/blog/probuse-odoo-apps-25/post/odoo-website-cash-on-delivery-shop-ecommerce-510

https://apps.odoo.com/apps/modules/11.0/website_cash_on_delivery/ 

Regards,

More than it have you set up scheduled delivery facility?  I suggest you this one for you https://www.odoo.com/apps/modules/browse?search=Delivery Date Scheduler