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We have a widget that lets you save a home screen icon for iOS devices: http://widgets.jotform.com/widget/add_to_home_screen. Unfortunately, I'm not sure if this will prompt you to select a custom icon.
A workaround would be to use icon changer apps:
This will allow you to change the icon in your Android/iOS devices. The only downside is you cannot publish the same to your end-users.