Not a new thing in US society, to use ridicule. Remember the public stocks:http://etc.usf.edu/clipart/12300/12397/stocks_12397.htm
I think if Disney catches a wayward gun owner packing inside a Disney theme park, that a public stocks in Wild West World might be appropriate.
Detain the guest, perhaps with a hood, plastic handcuffs and drag them off to the dungeon in Tinkebell's Castle for a minimum of two hours with no water, no cell. Then put the low life specimen in a silly baggy outfit in the public stockade with duct tape over their mouths (so as to prevent a flow of profanity), for another hour and a half.
If said nasty little perps ever come back to the park with their piece again, a bullet through the head would be merciful compared to what Goofy will do. That would be the rumor anyway. Giant billboards around LA with unflattering mug shots of adults caught on Disney property with weapons would be a next step. Side shot, front shot, holding a number.
Note: if you're in a public space and the state says packing in public is OK, fine. But when you enter a private space, different rules may apply and if you can't fathom how that could be, then stay away until you figure it out.
Note: I am not a an employee of Disneyland and the treatments described above are for rhetorical / satirical purposes. In sketching a science fiction alternative reality, I am not divulging actual plans by the owners of Disneyland to enforce private property rights when appropriate. Read the official documentation for specific language and the list of prohibitions.
Also note: if I were actually advising, my counsel would not be the above (Wild West World does not exist, must be thinking of that movie with Yul Brynner -- nor is the Castle technically Tinkerbell's). Discovery of a weapon on a guest's person should be treated no less liberally than discovery of marijuana cigarettes, which the state may also allow to be bought and sold with a permit (just like the gun and tobacco). Offer to check the gun (or weed) in a friendly manner in one of the many lockers at the perimeter of the park. Ask for ID and scan it, keep a database, share with public authorities. Remind the guest of park policies and the option to take disciplinary action if repeated offenses become the issue. Screen the above science fiction in cartoon trailers to focus groups, reminding people of time-honored park policies. Do not let the deterioration of North American civil society pop the Disneyland bubble as the Happiest Place on Earth.[tm]