The TDA cabinet has at least 2 jacks, labelled EPG and MOH. Guess what MOH means :-)
I don't know about cost effective, but you can get an MP3 player or use a spare PC to stream MOH music to your phone system at prices starting as little as $29.
lists players that sell for $140-200, and the Software tab gets you Message Studio to make your own MOH productions. It includes free music and voices.
Outside of that, use the keywords MUSIC ON HOLD and you will see tons of prices and alternatives.