You have to start as an illy and then betray to a coercer, yes. Coercers are an evil-only class, so you'll never be able to become a Kelethin (or Qeynos) citizen as a coercer. You'll have to pick Freeport, Neriak or Gorowyn (the evil cities), or once a coercer start the betrayal process (becoming exiled, living in Haven and being KOS to both sides) and never finish it. The choice to choose a class gets offered as the last step in betrayal (however becoming exiled and KOS in both good and evil cities happens as part of the first step).
Note that there's also the arasai, basically evil fae. If the appearances and abilities are OK you could take that race and start on the evil side. Either way, there's no way to be a coercer and live in Kelethin. Kelethin's a good city, coercer is an evil-only class and you can never become a citizen of a good-aligned city while your own alignment is anything other than good.
Note: the above applies to PvE. On the PvP servers there's a different ruleset that does allow you to betray an evil-aligned character to a good-aligned city without changing class. I'm not sure how the mechanics work, I don't do PvP.