The renter would have the burden of proof to show that you did discriminate.

You can counter offer with different terms if the prospective renter offered something other than you first offer to all possible renters. So since you asked for x and he offered y, now you can counter offer with z as the rent amount and any other changes to other terms if you wish. Or just reject his counter offer for being lower than the asking rent and then change your rental posting with your agent for all prospective renters.

If you change the terms for this renter you do not have to change your listing, you are in negotiations with this one person only. You can either just refuse their offer or make a counter offer. Once you make an offer to this prospect, you can state that they either accept or deny you will not take any counters on this last offer.

But if you refuse or make a counter offer and they decide not to accept the counter offer, you can change your listing if you want to, but it is not required.