Many of the buildings at the Grand Canyon are federal, you can't bring a firearm inside.
Aside from that, you shouldn't have any problems carrying anywhere else in the park.
I've carried there several times, including trips to Phantom Ranch and back without any issues.
Are you going below the rim, or just enjoying the views from the top?
If you are going to hike into the canyon, I would suggest the South Kaibab trail, the views are much better than the Bright Angel trail.
A hike to Skeleton Point is a good day hike, pack a picnic lunch and enjoy the amazing scenery, you can see the Colorado River from there.
Skeleton Point Pictures
Take lots of water and remember, it takes twice as much time to go up!
Enjoy your visit!
p.s. If you hike the trails, watch out for Mule Pools!