Can a landlord ban a tenant from using the backyard?

Yes, you can put such a provision in the lease but that will probably make it difficult to find a suitable tenant.

You can restrict your tenant's use of the yard by putting that prohibition in the lease. As Mr. Chertock has pointed out, however, this may limit your ability to rent the apartment and the amount of rent you can charge. You may want to consult your neighbors to see how they deal with this issue.

You can do this without a problem. However, that might limit how many people wish to rent from you.