They would be 4 8-way joysticks.
By that do you mean 8-way joysticks for 4-players or 4/8-way switchable?

The more clearly you communicate what you're looking for, the more likely you are to find exactly what you want.
Do you want:
Motorized 4/8 switching Y/N/Doesn't matter
Above panel switching Y/N/Doesn't matter
Below panel toolless switching Y/N/Doesn't matter
Below panel switching w. tools Y/N/Doesn't matter
Preferred type of joystick? ________________/Doesn't matter
Commonly played game genres? ________________ (Fighters, SHMUPS, etc.)
Other:____________________________
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PROTIP: Too much detail is better than not enough.
Scott