What's is a good, working PS2 emulator for a Samsung J3 Prime?

There are only 2 PlayStation emulators available at this time.

PCSX2 (windows, mac linux) and Play! (windows, mac, linux, android, ios)

The samsung J3 is an android phone, thus the only option for ps2 emulator for you is Play!. However, Play! is only being developed by like 2 people and was just started on a couple of years ago, its not really ready to play games yet. It can play a few games, but it is slow and buggy. Also I'm not sure the Samsung J3 could even handle full speed ps2 emulation even if there werre an emulator capable of it on android. Ps2 emulation is quite cpu heavy, and phones generally have far weaker cpus than most desktop and laptop pcs. Maybe like the samsung galaxy 9 or 10 era phones could maybe handle it. So a higher end flagship phone from like 2019-2020 maybe?

Either way, it will probably be until like 2020 before an emulator capable of play ps2 games rather well is available on android, it will take that long for the hardware to also catch up enough to play gamecube and ps2 era games.

The best you can do right now is a windows tablet device with a modern intel cpu. Personally, I have a dell latitude 1575 tablet. Its able to play PCSX2 at relatively full speed for most games. That tablet is a few years old now (still pretty good, much betetr than android tablets), and there are the newer 8th gen intel cpus available which are even better and more power efficient than the one i have, so it will probably do rather well with gamecube and ps2.