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Tool/Store that can provide unique time slots per customer?

Hi community,

I have recently created a website that I was initially told was merely informational. However, the client now wants to add an ecommerce store that allows the customer to purchase his product and select a delivery slot (1 slot per customer) which then removes that slot as available from other customers. I do not have the coding expertise to accomplish this and so I am asking for your advice on plugins, or apis or anything that can be installed to achieve this result

Hoping the experience of you wonderful lot can pull me through here!

Thanks in advance.

Here is my site Read-Only: [LINK]