"You can't be in two places at the same time."

Suppose TheCoin was distributed at a specific time of day (say local solar noon for every degree of longitude).  Each potential recipient would need to undertake a few actions that take a few minutes, that they could not in general physically do with two or more devices.

For example, they might have one minute in which to log in, after which they would receive a series of instructions directing them to a random series of positions reachable by walking for a few minutes total (by which time the password entry and start walking window would be long over).  Sometimes they would be directed to take a picture in a specified direction.  Sometimes they would meet someone else and exchange random codes to be entered into their devices.  Etc.

Some would attempt to get around this by hiring poorer people to do it for them (similar to gold farming).  One way to reduce the value of this, would be to only pay out TheCoin randomly, averaging once a week.  Anyone who wants to hire others to do this would have to hire them for every day of the week, even though they only get TheCoin once a week on average.  (Longer term, the problem is mostly solved as networked mobile devices get common and cheap enough for all - why do it for someone else? )

In addition to the above control on distribution, TheCoin system might require some small amount of work to earn the distribution, such as running a light weight server, or doing mechanical turk things such as examining photos to verify they were taken where claimed, or show a person matching a photo of the person who claimed to be there at a specific time.