As a musician, there's only one way that I can think of to do that. You'll need some sort of digital delay device, available from most major music stores (e.g. Steve's or Long & McQuade). The easiest to use, because of its portability and relatively low cost, would be a digital delay pedal, and you'll need a model that allows you to separate the delay from your original signal (otherwise you'll end up with a mix of both signals).

I'm assuming that the amplifier you would run the DVR audio through has its own radio receiver built-in, and that it's through this receiver that you'd normally listen to the radio. If that's the case, then for a setup like this, you'll need a separate radio, preferably a portable one for ease of setup.

Run the radio signal through the digital delay pedal and set the pedal so that it repeats the signal only once. Plug the output you want, delay signal on its own, into a vacant set of inputs on your amplifier. The next time the game comes on, look for a "delay time" knob on the pedal--you should be able to adjust it so that the radio signal is in perfect sync with the video.