This page has directions for how to delete Pokemon save files for every cartridge/console to start a new save, including how to redeem multiple Manaphy Eggs from Pokemon Ranger.
Delete a save file from a GB/GBC cartridge
Start a new game and save. This will overwrite the older save file.
Delete a save file from a GBA cartridge
Start a new game and save. This will overwrite the older save file.You can also hold Up + Select + B on the title screen.Alternatively, you can use homebrew on a Custom Firmware Wii to erase the save file.
For Pokemon Ranger, deleting the save file will not make it possible to claim another Manaphy Egg.However, with a Custom Firmware 3DS it is possible to reset the cartridge entirely.
With Pokemon Ranger inserted, go to FBI -> titles -> game.
Go to erase save data and press A.
If you use Checkpoint to back up the save right before transferring the Manaphy Egg you can easily get the Manaphy Egg repeatedly.
Delete a save file from a 3DS cartridge
Hold Up + B + X on the title screen.
Delete a save file from an Nintendo Switch
Go to the HOME Menu and select "System Settings".
Scroll down and select "Data Management".
Choose "Delete Save Data".
Select the game title you want to delete the save data for.