Hi Roro, I had spoken regarding this to renter in Karol Bagh last year. His reply was, since only a few people are interested in hiring these motorcycles, renters don't like to keep them. They instead prefer Enfields, which majority of the people are looking for. However he did said that if some one was looking to hire a CBZ/Pulsar/Karizma for more than a couple of weeks, it can be arranged, however he would need at least 2-3 days for it (buy and service the vehicle).
So unless you come across a person who has ready stock of CBS/Pulsar/Karizma to rent out, chances are that you would have to either buy a second hand motorcycle from a dealer or once again take an Enfield.
Having said that, you can try giving this guy a call and see what he has to say:
Jitender - 9810550243. Charges a decent price but his bikes are super well maintained. He's my mech - does service backups for RE for Himalayan Odyssey, Raid de himalaya and all that. Good knowledgeable fellow and you'd get good bikes. You can give him my reference.