Decline his request to rent it as a separate contract. Make the shed agreement as an addendum to the lease. If he leaves for one reason or another, he will be required to remove the shed as well. Failure to do so could lead to the shed to be considered to be abandoned. This is his incentive to get it moved.
You do have a choice here. You can also just say no. If the shed was important, it is something he should have considered before the unit was rented.
One other thing to consider, installing a shed in a grassy area will kill the grass. You may want to include a clause that states that he will be responsible to pay for time and materials to reseed and care to bring the lawn back to original.