Is it possible to create a MongoDB replica set consisting of only 1 primary and 1 secondary member? I would like to have delayed replica set that will copy data from primary
Yes, it is possible but not recommended. The caveat of this approach is no automatic failovers.
If you primary goes down then you will have to manually make the other server as primary.
If you are keeping you secondary only as a mirror of your primary and you are fine with manual failover then it should work for you.
More info here:
http://openmymind.net/Does-My-Replica-Set-Need-An-Arbiter/