You have two options:
- buy more memory cards
- buy portable storage
Yes, there are other possibilities, but with not under the conditions you have set forth.
The first is the cheapest. Now, it is dependent on your camera and avg file size but figure ~1GB per day. This assumes you will NOT do any movies in the camera. If your camera uses SD cards, I'd say 4-6 2GB cards - at ~$11 each. Not 2 4GB cards. If one does go bad, you stand to lose more shots. More, smaller cards can mitigate the risk.
Portable storage is something slightly larger than an iPhone. Basically a small harddrive with a card reader in it. Some have a viewing screen too.
The cool solution would be a WiFi card to load pics right to the web. Not gonna happen in the parks though.