There does not seem to be any replacement batteries for sale for the Dell DJ. I did some research and found that the Dell DJ Pocket DJ uses a Lithium Ion battery type LP043048 with 500mAh capacity. The size is 30.5x48.5x4mm.
I used a replacement battery pack made for Apple Slim IPOD -3G. Apple battery number 616-0159 and E225846. Google 616-0159 and you can find many sources for this battery. I got mine on Ebay from Enessy/ Digital Power Pro for about $10. This replacement is 053048 so is 1 mm thicker but still fits. Also the replacement is a Lithium Ion polymer with about 850 mAh capacity, so this is good, longer run time.
The original pack has 2 wires, red and black for positive and negative. The replacement pack has three wires. Red Black and White. The white wire is for thermister in the battery assembly that we don't need. The connectors are not compatible and the wires are too short so you have to cut the red and black wires for the old connector and solder them onto the new battery. Just cut and remove the white wire. Take care not to short the battery. Use heat shrink tubing to insulate the splices. Also use insulating tape to make sure that no part of the metal battery is exposed and can touch to any of the Dell DJ circuits. Take care not let the battery short or overheat it when working with the heat shrink tubing. Lithium batteries can be dangerous. The wires are very small, you need to know how to solder and strip small fine wires to do this.