Following is the code for the copy image into pasteboard
NSData *data = [NSData dataWithContentsOfURL:[NSURL URLWithString:@"http://warp.povusers.org/images/test.png"]];
UIPasteboard *pasteBoard=[UIPasteboard generalPasteboard];
[pasteBoard setData:data forPasteboardType:@"public.png"];
Now the think is that create extension of custom keyboard in that layout you can put your UIButton and that button action implement above for png image.
For Local Image following code is help full to you and it's working in my case.
UIPasteboard *pasteboard = [UIPasteboard generalPasteboard];
NSData *imgData = UIImagePNGRepresentation(@"Your UIImage Here");
[pasteboard setData:imgData forPasteboardType:[UIPasteboardTypeListImage objectAtIndex:0]];
More Uniform Type Identifiers you visit here and change Pasteboard Type.
May this help lot and solve your problem.
Edited
"Allow Full Access" From Settings -> Keyboard -> Keyboards -> select your app keyboard -> On switch of "Allow Full Access"