The standard way to add user data to an Arnold node is to add an mtoa_constant attribute to the shape node in Maya. MtoA translates the mtoa_constant attributes to user data, so you can use shaders like AiUserDataColor.
Instances in Maya, however, don’t have their own shape node: they all share the shape node of the original object. So you can’t use an mtoa_constant attribute on the shape to get different user data for each instance.
But you can use override sets to get user data on instances. Put the instances in a set, and then add the mtoa_constant as an override attribute.
Then each instance in the set will get that user data.
Another way to add user data to instances is with the particle instancer: you can add per-particle attributes, and then list them in the Arnold > Export Attributes text box. MtoA translates all those attributes to user data on the particle instances.