After the 5/21/2013 system update I had to redo the su install, as it wipes the system.
The first step is to install su and busybox.... Or to setup your computer for adb...
To get google play music you need the 3 files listed below, I pulled the login and framework apks out of a 4.1.2 gapps zip.
the files are in /system/app
The music apk can be found here... or do a quick google...
Put the files in the same folder as adb.exe you used in the su busy box install.
0. Connect to the device. if you followed the first link about su you should have wireless adb.
adb connect 192.168.xxx.xxx
1. Push the files over to the sdcard.
adb push GoogleLoginService.apk /sdcard/.
adb push GoogleServicesFramework.apk /sdcard/.
adb push com.google.android.music-1.apk /sdcard/.
2. Open a super user shell.
3. Copy the files over to the system/app directory
cat /sdcard/GoogleLoginService.apk > /system/app/GoogleLoginService.apk
cat /sdcard/GoogleServicesFramework.apk > /system/app/GoogleServicesFramework.apk
cat /sdcard/com.google.android.music-1.apk > /system/app/com.google.android.music-1.apk
4. Set permissions on the system/apps files.
chmod 644 /system/app/GoogleLoginService.apk
chmod 644 /system/app/GoogleServicesFramework.apk
chmod 644 /system/app/com.google.android.music-1.apk
5. Exit and reboot.
6. When you launch the music app it will ask you to login to your google account.
*remember any future updates will most likely remove any changes you made to system.
** I ran this on the 328 ota and got a few googleframework FC's when signing into google, I just closed out of them and its ran fine since.
*edit - typos, thanks zdraw
**edit - efficiency/least privilege permissions