Easiest/Fastest Infamy IMO

[TJs]

All you do is stand close to a stable hand and kill another players mount over and over. This costs no labor and is so fast if you don't have clowns trying to gank you in the process (good luck). I recommend getting a new fresh mount (or several) so that it's level 5. The higher the level of the mount, the higher the cost to heal it at a stable hand. This will not work killing it over and over at 1 HP.

I heard Karkasse is the best place to do it, not sure where exactly. I found out about that long after I decided not to become a pirate. When I was doing it with a friend we were in Cinderstone and stood on a Nui statue by, I believe it's called Seachild Wharf? I would kill several lvl 5 mounts, then stand on the statue while he ran the stable hand to revive. This kept people from ganking me while I was flagged and also if they saw I was wanted, thus sending me to jail prematurely.

Couple pirates I've talked to got pirate in about an hour or two from 0 doing it this way in Karkasse.

Also, off topic, if you die with over 2k crime points you get a hilariously long jail sentence. Longest I've seen in game so far was 1,464 minutes.