Let's make sure we understand - you are trying to make arrangements for your customer on their behalf and you are not just trying to get a room for yourself? Since it is in this forum, can we assume that it is a Marriott property?

The most straightforward way to handle this is to simply tell your customer that the hotel is sold out and offer to make alternative arrangements. As long as this is honestly the case, I don't see the problem.

If your customer happens to be Platinum with Marriott, then have them book a room with their guarantee.

If you want to take a risk, you can try booking withing 48 hours of the arrival. That is when they will free up any rooms they were holding for the Platinum guarantee. Also, if there was a convention tying up a lot of rooms, they may release unsold inventory prior to your planned arrival.