I may have found a program that does direct to CD audio recording, but feel like I need to ask you to not try this approach, and consider a normal recording workflow.
If you're sending audio to the CD burner, then you're in HUGE danger of losing your recording if anything goes wrong with the computer, or with the disk. It seems like you're choosing between either getting the recording, or getting the cd "immediately". Given that choice, I'd always choose to get the recording. Even if some program was able to clone the audio stream and save a backup to your hard drive, I'd still be scared of using it, because who knows what would happen during a power failure (how long to reboot your recording setup?), or a system crash caused by an AWOL CD burner.
If your customer is trying to make CDs quickly (say, after a concert), then it's still a better idea to bring a duplicator with you, and hit the record button as soon as the audience starts their final cheer. It's just hard to imagine a situation where the priority would be on MAYBE getting a disk now, instead of getting a disk in just a few seconds.
The program I found was made by... well... I have no idea. There's a complete lack of addresses or other identifying locations or names on their website. Considering your personal financial safety, it would be insanity to order anything from a company with just a website and an email address, especially if a client was going to rely on it.
If all of this still didn't dissuade you, the program is called Direct Audio CD, at softgogo dot com.