Here's what you need:
Ziatron and SoccerRef mentioned these products earlier and they work great:
1. The HDFury3 (or HDFury4) will convert your Apple TV 2's HDMI output to analog component video (Red, Green, Blue) and analog stereo audio (Red, White). To hook your Apple TV 2 up to your older TV with component video input, you would need an HDMI cable, an HDFury3, and a component video cable. Keep in mind, your TV must support 720p video through its component video input and you may have to adjust the audio settings on your Apple TV to output PCM audio (not sure if HDFury3 will process Dolby Digital or DTS bitstreams). Also, HDFury3 costs $250... once you also factor in the cost of an HDMI cable and a component video cable, maybe it makes more sense to just get a more current TV. Used plasma and LCD TVs typically sell for about half price after about 2 years or so. I just saw a couple 42" plasmas (with HDMI inputs) for under $350 on craigslist.
2. The Gefen Toolbox GTVDD2AA optical (Toslink) digital audio to analog stereo audio adapter is excellent for converting digital audio to analog stereo audio (Red, White). I've used this with Dolby Digital and it works great.