There are like 25 games that are confirmed to work on 4.81 (without a second ps3) and there are probably more games that can be working by this same method.
Anyway first of all : Don't update your ps3 sony launched 4.82 update today and it may block this method so please don't update.
Alright now this method consists of injecting games into your backup so ur gonna need a usb flash drive/external hard drive that needs to be formatted in fat32 format (check youtube on how to do that), and ur gonna need a software that would allow this injection TABR is the best software till this date here is the download link:
https://www.psxhax.com/threads/true...ler-v2-30-ps3-update-by-jjkkyu-released.2919/
and now you have to open it and it will create like 10 folders (backup , game , edat, idps etc) So now lets get started : first thing is you need to download a game from this list:
http://www.pspx.ru/forum/showpost.php?p=1110029
usually you would have to patch (crack) the games yourself but thanks to the community some people upload their patched games so other users can just download without dealing with anything else.
okay now after formatting your usb/hard drive to fat 32 , you put it in your ps3 and go to system -> backup and restore and choose backup. after several minutes (or hours depending on what u have installed in your ps3), you take your usb drive and u will find folder called ps3->export->backup and u will find a folder with a name that consists only of numbers (example 201711141915) so now you copy that folder and put in a folder called backup under your TABR folder that we just downloaded earlier. now you copy the game you downloaded and place it in the folder called game under TABR folder.
Now finally you run TABR and press 1 to choose the backup , and then press 4 to add the game and finally press s to inject the game into backup. when it's done u will find yout backup in a folder called export under TABR so now you just copy and paste it in your usb/hard drive and then connect it to ps3 a and go to settings , backup and restore and choose restore and boom your game is there. Hope i helped