I just tell them what Geocaching is and email them the basic information. That's it. This last time I described a flat little magnetic key holder under a picnic table. The time before that, the guy called his insurance company and they said no. He actually told me that he wouldn't allow High School car washing for fundraisers for the same reason. It's all about someone suing them if they get hurt on the property.
I'll tell you why I want to ask permission that's because I was looking for a cache one day. I looked up not, one but 2 cops. Fortunately I look pretty harmless.
So I'll turn this around. How do you all ASK? How do you get that yes?
First off, thank you for asking for permission. That's an important step in cache hiding that is ignored far too often.
Second, the "cache at your own risk" wording only excludes Groundspeak from being sued if someone gets injured or dies while geocaching. It doesn't protect the landowner.
Third, how are you presenting your cache to the landowner? And how is the cache going to be hidden? If it's something generic like "I want to hide a cache on your property, do I have permission to do so?", why would that landowner immediately jump to thoughts of liability? If you said something like "I want to hide a cache up in a tree on your property", then, of course, they're going to think about someone falling out of the tree and the liability for injuries that occur on their land. If you are trying to hide "dangerous" caches, I would expect many landowners to balk at giving permission.