You can go to radio shack or if you have a local electronics store, and buy you a roll of 300 ohm twin-lead tv antenna cable. If you can get the stuff without the foam injection plastic thats better, but it doesn't matter.
I have a link here that will show you how to make a cheap and very reliable GAIN antenna known as a J-POLE, that will work well on VHF and UHF. All you need is a knife, some solder and a soldering iron. What you'll be making is a vertical VHF 5/8 wave over 1/4 wave dipole antenna. Best of all, its very flexible. You'd be able to roll it up and put it in your pocket, then when needed pull it out, string it up on a mast or up a tree or anything, and attach coax to it and to the radio. It'll be at least 5 times better than the included antenna with your scanner.
Here are the instructions with diagram:
http://larc.hamgate.net/pocketJpole.htm
http://www.qsl.net/wb3gck/jpole.htm
Here's how to make one with 3/4 copper pipe...
http://www.dxzone.com/cgi-bin/dir/jump2.cgi?ID=3481
Remember this, DISCONE antennas do not have any gain, they are uni-gain antennas. The only benefit to a discone is being wide-range. It will work on several frequency bands. But if you're limiting your listening to just VHF and UHF, the J-Pole will be better because it has gain. At least 3 dbi or 7 dbi gain depending on the model you make. That could mean a great deal when trying to pull distant stations in. Discones are also rather difficult to make because you need a lot of machined parts.
Another thing you could do, but it too would have no gain, would be a 1/4 wave vhf ground plane. All you'd need is an SO-239 chassis connector, and some solid copper wires, about 14-12 guage. You'll need to cut 4 pieces at 20 inches, and then 1 piece at 18 inches. You'll need some pliers, 4 small screws with washers and bolts, a soldering iron with solder.
Take the 4 20 inch pieces and on one end of all 4, with pliers bend the tip back onto itself so you make a small eyelet (a hole for the screw to go through). Take the SO-239 connector, and all 4 20 inch wires, place the bent part over each corner of the so-239 connector where the chassis mount points are. you'll want to put a washer over the wire, and another washer on the other side of the chassis mount, then push the screw through, and take the bolt and tighten it down. Do this for all 4 wires in all 4 mount points on the SO-239 chassis connector.
Now you'll want to take all 4 of those wires and carefully bend them down into a 45 degree angle from where they're mounted onto the SO-239 connector.
Take the 1 18" wire and place it into the center point of the SO-239 connector and using solder and a gun or iron, solder it into place this will be the vertical part.
The other side of the SO-239 is where your coax will screw in....
Take the SO-239 with all of the radials attached to it, and set it on top of a small pole. Have your coax go through the pole to the other end, fasten your coax to the SO-239 and then have it sitting on top of the opening of the pole. then just keep tension on the coax so the antenna stays in place. Mount the small pole (small meaning 5 inches or something) with u bolt brackets attach to a mast of some type... And there you go...
the j pole is better though.
Not sure what an SO-239 is? RADIO SHACK sells them, look at the pic here to get the idea what I'm trying to describe.
http://www.dxengineering.com/images/prod/so-239_parts.jpg
You'll see 4 holes (mount points) on the SO-239. thats where you're going to bolt the 4 (20 inch) wires to with a small screw and washer/bolt set. and then you see the center conductor point, just solder the other 18" wire in there. and you can clearly see the part where the PL-259 coax would screw on.. allow the connected coax and tension keep the antenna in place.