I have the same problem previously reported and solved for Ubuntu 18.04 here: PCSXR works fine with one controller, but when the second controller is connected, the plugin window does not open and the controllers dont work. This bug was originally reported and solved (for Ubuntu 18.04) here by Josefien. The solution involves:
In the last post of the bug report, Josefien mentions that she successfully applied the same process to fix the problem in Ubuntu 20.04 so I was encouraged to try this.
Unfortunately I could not make it work. One of the problems that I had to overcome was finding the files, as the link provided in the post ( https://packages.ubuntu.com/xenial/pcsxr ) does not seem to work anymore and I could not find them either in the file pcsxr_1.9.92-4.debian.tar.gz in https://launchpad.net/ubuntu/+source/pcsxr/1.9.92-4 (although I am aware that I may be looking in the wrong place). To get the files I installed PCSXR on a bootable USB with Xenial on it and get the files from that installation (but I am really dubious that this method will give me the right files).
After using those files as described in the previous post, and installing libglade2-0 this is how my psemu folders look like:
/usr/lib/x86_64-linux-gnu/psemu$ ls -l
total 1112
-rwxr-xr-x 1 root root 18360 Jul 17 2018 cfgBladeSio1
-rwxr-xr-x 1 root root 18360 Jul 17 2018 cfgDFCdrom
-rwxr-xr-x 1 root root 30928 Aug 7 23:12 cfgDFInput
-rwxr-xr-x 1 root root 22456 Jul 17 2018 cfgDFNet
-rwxr-xr-x 1 root root 18360 Jul 17 2018 cfgDFSound
-rwxr-xr-x 1 root root 22456 Jul 17 2018 cfgDFXVideo
-rwxr-xr-x 1 root root 30648 Jul 17 2018 cfgpeopsxgl
-rw-r--r-- 1 root root 22376 Jul 17 2018 libBladeSio1.so
-rw-r--r-- 1 root root 30600 Jul 17 2018 libDFCdrom.so
-rw-r--r-- 1 root root 22504 Aug 7 23:12 libDFInput.so
-rw-r--r-- 1 root root 22368 Jul 17 2018 libDFNet.so
-rw-r--r-- 1 root root 55320 Jul 17 2018 libDFSound.so
-rw-r--r-- 1 root root 412824 Jul 17 2018 libDFXVideo.so
-rw-r--r-- 1 root root 381312 Jul 17 2018 libpeopsxgl.so`
and
/usr/share/psemu$ ls -l
total 248
-rw-r--r-- 1 root root 18522 Jul 17 2018 dfcdrom.ui
-rw-r--r-- 1 root root 24012 Aug 7 22:41 dfinput.glade2
-rw-r--r-- 1 root root 39739 Jul 17 2018 dfinput.ui
-rw-r--r-- 1 root root 15165 Jul 17 2018 dfnet.ui
-rw-r--r-- 1 root root 19971 Jul 17 2018 dfsound.ui
-rw-r--r-- 1 root root 40310 Jul 17 2018 dfxvideo.ui
-rw-r--r-- 1 root root 72322 Jul 17 2018 peopsxgl.ui
-rw-r--r-- 1 root root 14160 Jul 17 2018 sio1.ui
But the Plugins and Bios Configuration Window looks like this, with the dropdown widget for the Controllers empty.
I would appreciate if anyone could provide any guidance or suggestion.
Thank you for your help!