An easy and convenient way to achieve the described scenario would be to check in
event handler for any appointments in that time slot.
Getting the DOM
element for the clicked time slot and check if has attribute with your custom class will show your context menu that contains "Make available" option.
Please find attached a sample project that demonstrates the desired functionality implemented by using three different RadContextMenus
depending on different conditions.
Hope that this will lead you into right direction.
the Telerik team
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