Our bank has several customer that are operaters of Privately owned ATMs. What are we required to do?

Track their volumes to ensure that they are consistent with the size of their business/location/clientele.
If necessary, get a copy of their contract.

Check out the Banker Tools page, there's a checklist there that may be helpful.

The bottom line on this type of activity is that you need to know who is responsible for replenishing the cash in the machine (either your customer or their IOS) and if it is your customer you need to know where the cash is coming from. If they have 1 or more ATMs as their only business they should be withdrawing the same amount of cash from their account with your bank to fill the ATM. If they have a business such as convenience store, etc you will need to assess if their business volume could generate enough cash (probably good quality 20's) to place in the machine. As MagicCity advised, getting a copy of the agreement is always important since the agreement specifies things like location, who is responsible for the cash, etc. Also, an examiner once stated that if the customer places sveral machines in various stores, businesses, etc. it is advisable to make a site visit to determine if the traffic in each business is commensurate with the usage in the machine.

Depending on where you're located, your customers may also be required to register/license the terminals with your state. It's a requirement in MA, and evidence of registration is one of the first things asked for by examiners/auditors reviewing these customers.