Not on the checkout page, unless you're a Shopify Plus member you cannot edit the checkout page. You could alternatively do it on the cart page, will probably want to edit cart-template.liquid in your sections folder.
This is an accepted solution.
When you set up your shipping options, do you create your own? If so, you can actually rename the Shipping method to include the delivery times in parentheses. For example, let's say you had the following shipping options:
You can rename them to include the general shipping times for each one. Changing it to something like:
Standard Delivery (5-7 business days)
Xpress Shipping (2-3 business days)
This will give you customer expectations on their order delivery time! You can follow a guide here that will show you how to edit your Shipping rates. If there is anything else I can help you with, please let me know.
Solid suggestion from @Dirk -- should have thought of that.
I'd just like to offer an alternate option.
We've created an app called Supertime that lets your customers select dates and times for delivery. You can create custom schedules so they can only select dates and time slots within the parameters you have set. This gives your customers the convenience and delight of having control over when their receive deliveries, and allows you to create schedules that work for you.
These dates and times can then be surfaced in our other app EasyRoutes that turns your orders into local delivery routes in seconds.
We offer free trials for both so you can see it in action first. Hope this helps!