Usually a couple of days is just a sufficient amount of time to visit/see the park itself. Thankfully at this point they still have not implemented a reservation system to enter the main canyon/or to hike the popular trails.
There are out of park activities of which the main one is canyoneering, and to a lesser degree hiking and sunset/hummer tours. They would have to be booked in advance to register a guarantee.
Gear for hiking the bottom up Narrows might need advance reservations. I have not heard any high demand for any other type of gear or bike rentals.
There is a horseback trail ride in the park of which I have no idea how popular it is. But you would still want to book that in advance at canyonrides.
You do not need a guide to hike in the park, even tho there is a few select routes.
Having never booked any activity at Zions I can't really say. And things have changed even in the last three years as far as number of people visiting, so hard to know for sure.
Since canyoneering trips are limited however if that is something you really have on your radar I would book that.
The horseback rides from Zions Lodge did not need to be booked anymore than a day ahead a few years ago.
My feeling is that with only a couple of days I would not necessarily need to fill the time up with extra activities. The park itself is enchanting. I would recommend you rent some bikes (again just a day notice should be fine). and if possible put them on a shuttle riding it to the end of the canyon and then ride the bikes back down the canyon. It is a great way to experience the park away from the crowds.
With only a couple of days at Zions, I’d focus on activities inside the park. No reservations needed.
Thank you for your input!