MongoDB cross datacenter replication without elections or high data availaility
You could created a Replica Set with a Hidden Member. The hidden member will take a read/only copy of your data. However, if the hidden member goes down then the primary steps down to secondary, i.e. your MongoDB becomes read/only.
You can define an Arbiter. It is not necessary to create the Arbiter service on a dedicated host, define it on your primary node. It is just a small mongod service which consumes almost no CPU/memory resources or disc space.
If you have a Primary + Arbiter on one host and the Hidden Secondary on another host then the second may stop and your application continues running normal. Of course, is your primary goes down then the application is not available anymore.