The rule that resolves nearly all of these: never lower the price without changing something on the other side.
A discount given for nothing teaches the buyer that your price is negotiable, which means it will be negotiated again at renewal and every renewal after. A discount traded for something is a different deal, and everybody understands it as such.
Things to trade for:
A longer commitment. Two years instead of one, at the discount. Very common, easy to justify, and it is genuinely worth something to you.
Payment up front rather than monthly or on terms. Cash now has real value.
A case study or a reference, in writing, with a date. For a first big customer this is worth a great deal.
Fewer seats or a lower tier. If they want to pay less, they can have less. This is the cleanest answer and the one people forget: the price is not too high, the package is.
A pilot period at a reduced rate that converts to full price on a stated date.
Any of those lets you say yes without saying my prices are whatever you push for. And the request itself is not an insult - procurement teams ask as a matter of routine, and a good number of them expect a no.