Well, everything depends on if the people reading your ad don't like it. They could flag it for any or no reason, and trolls DO exist.

1. You could be vague enough in your ad that those reading it wouldn't necessarily guess what your advertising is an MLM opportunity. This way you would potentially get more people responding to your ad, but that would entail more time for you having to send out replies.

(I'll say it again, Craigslist does not want those ads on their site.)

2. You could purchase some Craigslist "phone verified accounts." There are people that sell already set up accounts, as well as software that lets you create fresh Craigslist accounts. Just search for Craigslist PVA or Craigslist phone verified accounts. There are some services that promise to replace the account with a new one if you get banned.

So how do you go around it?

Technically, that's not allowed according to their Terms of Service. Yes, there's a LOT of crap on Craigslist, but it's very easy to get flagged, have your posts removed, and ultimately have the account banned.

I suppose it IS possible (since lots of people do it), you just can't do it playing by the rules.

... and I wish it weren't so!

See last bullet:
http://www.craigslist.org/about/prohibited