This is a simple NO UMD FiX by LightForce:
1) Extract Derby_Time_2006_JPN_PSP-Caravan to a folder on your PC using iSOBuster or similar utility.
2) From your original PSP_GAME folder move the ICON0.PNG, ICON1.PMF, PARAM.SFO, PIC0.PNG, PIC1.PNG, and USRDIR (with all the files inside it) to the DERBY2K6 folder from this pack.
3) Now follow the instructions as normal from the included NFO file:
Put the 3 folders to memstick and start runumd ....
NOTE: Although this is labeled a "NO UMD" release, that just means you don't need the actual DerbyTime 2006 UMD in the drive to play the game, however, you will need a UMD in the drive to run it (any UMD game should work).