well unlike the nintendo 64 emulators, there are still making games for ps2, and their is still alot of copyrights over games, most ps2 emulators are handled through piracy sites, the games too, all of which is illegal, it is hard to find a legit one, and even at that i don't even know if the 64 emulator was legal or not, no one will probbaly give you an answer, a little hush huish on here, but there was many others asking the same question you asked on here before, i saw at least 4-6 when i looked for this question. try them and see what they advise, if no one helps you here,
i have tried looking for one, never had much luck, found a place to get gamecube iso's (emuparadise.com) but...that was iffy. i never got them to work. sorry i can't be more helpful.
i hope this helps you
update: that is really what i said, like using software like Utorrent and using sites like :"thepiratebay" are perfectly legal seperatly, but when combined, illegal! i think you can find some ps2 games (mainly iso's) for download like smaller less popular games, but the bigger ones still have strong copyright on them (titles like say, guitar hero 5?), soon they will time out, and become free to the public, and the software like i read "pcsx" i have heard before i think, but i don't know.