Tl;Dr; The reason to include an actor in the story is to provide context on who it is benefiting. In this case, the site owner derives little, if any value from the story, so you'd go with the site viewer.
However, the reason this example is particularly confusing is that the story dictates implementation. A user story should describe the need being served rather than the way to implement it. In this example, we've already decided we want a carousel and we've completely lost the need being served. This is actually a pretty common problem with graphic design elements.
To make this a little more clear who benefits, we have to back up a bit. The carousel idea is usually used to draw attention to new offers, so a basic story would look something like this:
As a customer, I'd like to be presented with new offers in a highly
visible place on the home page so that I don't miss out on new deals.
In this story, it's clear that I'm trying to serve the customer by placing important and timely information in a highly visible area. But, there is no reason to create a carousel (or anything more than a basic banner). For that we have to look at the need it's filling. In most cases, it's so you can show a number of different deals without taking up too much screen space, so we have a second story:
As a marketing coordinator, I want to be able to display up to five
deals on the homepage without using too much screen space so that I
can run multiple specials simultaneously.
I still don't have a carousel, but the developers and designers will work together to find the best approach, which may be a carousel.
Note: There are a lot of angles to this. Maybe a carousel has been used many times and it's more work to do it as two stories, so you combine it back into one. I broke it out this way to specifically look at the question of who the story is for. If you combined it back into one story, I would still have the customer as the actor because the primary value is to entice the customer with new deals. The ability for marketing to create those deals is only a response.