I found a solution fitting my problem.
I added a udev rule like it is described in this answer to a similar question.
First I had to create a new group called leds. Then I created the udev rule in /etc/udev/rules.d/10-buzzers.rules (I created the file by myself, it did not exist before).
Since I wanted to only use the Buzzer LEDs of the Buzzer controllers for the Playstation 2, I optimized the rule to only affect the files for the controllers.
The rule only applies to devices that match the kernel information in the field KERNEL.
The rule executes chgrp and chmod that the matching device files are owned by the leds group and that the owning group has write permission.
My final rule:
SUBSYSTEM=="leds", KERNEL=="0003:054C:1000.[0-9]*::buzz[1-4]", ACTION=="add", RUN+="/bin/chgrp -R leds /sys%p", RUN+="/bin/chmod -R g=u /sys%p"