If you are using GReminders for Automated Scheduling you are able to embed this into your Website.
You can see on the right (or below if you are viewing this on mobile)
we have an embedded iframe which renders the booking application.
Just for the demo we have highlighted the iframe with a red border so you can see where it starts and stops.
Basically you can put code similar to this one into your web page.
<iframe src="XXXXXX" style="border: none; width: 100%; height: 800px; overflow: scroll;" allowfullscreen></iframe>