I have a client that wants to do this, however, the highest bit rate any of my
current software will do is 160kbps mono. Any ideas?

well, considering that you just have one channel, 160kbps mono is the same as 320kbps stereo

I know, but they were wanting the mono .mp3 file at 192kbps. I realize that the difference between the two would be practically imperceptible to the human ear, but I just want to accomodate the client.

LAME can do it and I just tried it. I used -b192 -mm with 3.96.1 and no problems.

Word.... thanks...

Not really. When you're encoding a stereo signal, redundancies between the two channels are eliminated, so you're not really encoding 2 full channels at all times. However in mono you're always encoding one full channel.

While it's definitely true that you can get away wth using a lower bitrate for mono than for stereo, you don't really get the same quality at half the bitrate.

yep, when Joint-Stereo is used, your statement is true

It's true even with Left-Right Stereo, though in that case, the savings aren't all that great.