Cd Recorder Operation

Rip the (CD) files to your computer using EAC (free program) You can rip the whole CD or just the tracks you want. You have to name each file yourself, so that adds a little bit of time. Stick them all in your 'music folder'
But then you can reassemble any collection of the tracks you want, then write them to a CD-rom.
No problem.
The fact you can post here means you have a computer.
Here is EAC: http://www.exactaudiocopy.de/
PS the first 'download' listed at the site is an ADVERTISEMENT, so read before you download.

Using a dedicated audio CD recorder is a waste of money.

I agree. I know that's not exactly how you wanted to do it, but the way Elizabeth recommends is really the best way to handle it.

My Tascam CD-RW700 allows me to do exactly what you're talking about. I assume that the newer models in the Tascam line will too.

I have a Pioneer Elite and a Denon Dual Tray that I have used many times to make compilation discs. On both you have the option to select "track" or "entire disc". So you slect the track and hit play or record depending on your recorder, being a single or dual tray. Very easy with good results.