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
Short answer: don't.
Long answer: the way automatic failover works in MongoDB is that a replica set needs a qualified majority to successfully elect a new primary. Delayed members do have votes in elections. So if either of your nodes fails the replica set finds out that it doesn't have this majority and the current primary steps down even if it didn't fail. So what you essentially do is doubling the chances of making your replica set fail. An arbiter is a very cheap process, in term of RAM usage, CPU and even disk space when run with --smallfiles --no-journal --noprealloc
or the equivalent options set in the config file. Note that the mentioned options are safe to use, since an arbiter essentially only checks the heartbeats of the data bearing nodes. You could put the arbiter on the application server for example.
Disclaimer: the following procedure is strongly discouraged to use. Proceed at your own risk.
You could set the votes of the delayed server to 0. This way the undelayed node will call for an election in case the delayed member fails, comes to the conclusion that it is the only node online of the replica set and that it has the majority of votes (1/1) and will continue to work as expected. This course of action needs some attention, as you will have an even number of votes again in case you add a member to the replica set later and makes it necessary to reconfigure the replica set. It also has serious implications with network fragmentation issues. Again: Use at your own risk