I am developing a site for a client who wants a media player with a few of his songs. - He wants the player to begin when the user first visits the site, and then continue playing as the user navigates through the page (of course with the option to turn it of if they so wish).

I am having trouble working out how to do this - as the player needs to continue smoothly between pages as it would be very disjointed and annoying if it were to restart every time a page was loaded.

I can only think of this being done with either frames or a pop-up window - neither of which are preferable - however i'm going with the pop-up option.
Does anyone have any other ideas of how this can be done?
I need to speak to my client about it in just under 12 hours.

There's no good way to do this, unless you indeed use frames or a pop-up. It's also not adviced to have music played the whole time, it usually annoys visitors more than it pleases them. If they want music, they'll click the play button, be sure of that.

you could also load your entire site in AJAX, but when done incorrect, this can mess up your Google ranking because Google can't read JavaScript generated contents...