This topic is too broad to be explained fully in this forum, but we will deal briefly with the major issues and provide a bottom line response. (We dealt with the topic more deeply in our book BeMareh HaBazak[1] regarding the related question of maintaining a monetized website on Shabbat.)
Lifnei iver (causing someone to sin): Although you speak of a machine to be used by non-Jews, it is not clear whether you refer to a location where some Jews will probably use the machines on Shabbat or where it is unlikely that any Jew will use them. Even in the more stringent scenario, there is ample room for leniency because of a combination of factors (each of which should not be relied upon independently): 1. It is likely that a Jew would be able to buy the same product from a non-Jew; 2. The main intent is for the non-Jewish majority; 3. Any Jew who would use the machine on Shabbat would do so knowingly and presumably regularly desecrates Shabbat; 4. You perform the actions of placing and filling the machine at a time when a Jew is permitted to use the machine.
Commerce on Shabbat: It is forbidden to buy or sell items, hire workers, etc. on Shabbat (even if the other party is a non-Jew) due to the concern that one involved in commerce may come to write, even if he does no physical action.[2] Some poskim say that one may not even make a transaction before Shabbat that will take effect on Shabbat.[3] At first glance, a sale will take effect on your behalf on Shabbat through your machine. However, others say that if the Jew is not involved in any act of commerce on Shabbat, it is permitted,[4] as is the case here. Furthermore, you are not doing anything to single out Shabbat as the day for the transactions to take effect, as you would presumably be happy if your machine sold out from purchases before or after Shabbat.[5] Some suggest that you should have in mind that the formal transactions not take place on Shabbat. You can accomplish this by intending that whoever puts money in the machine can take the desired item without formally receiving ownership[6] or by giving a present before Shabbat to whoever will put in money of the item he will select.[7] You can intend to take ownership of the coins after Shabbat. These poskim add that the machines should not be located in your domain or be publicly known as yours, although it is not clear why that is important in this case.[8]
S’char Shabbat: The primary prohibition of receiving payment for something that occurs on Shabbat is that one should not be paid for work he does then. If he receives money without having done anything on Shabbat, one could argue that it is not problematic. However, the Shulchan Aruch[9] says that a Jew may not receive profits from renting out an object for Shabbat, even if he does nothing on Shabbat. However, in our case, the payment is primarily to buy objects found in the vending machine. The prohibition of s’char Shabbat does not forbid receiving the value of an object that one gave to another, even if it was given on Shabbat.[10] (One has to solve the problem of doing commerce on Shabbat, as we did above). Even if one contends that in addition to the value of the object, one pays for the service of providing a vending machine, that extra payment is considered “swallowed up” in the non-problematic payment (havla’ah). Havla’ah of Shabbat pay is permitted.[11] (Parameters of that rule are beyond our present scope.)
In the final analysis, there are sufficient grounds to allow you to own a vending machine, at least in a place where most of its use on Shabbat will be by non-Jews.