Harvesters have Armor style health so heavy anti-armor weapons such as sniper rifles are preferred(If you're feeling brave, heavy pistols or really brave, shotguns). The Anti-Material rifles (Black Widow, Widow, or Javelin) should also be your weapon of choice as they penetrate armor thus eating it faster.
Your ammo choices should also be anti-armor as well, Incinerary and Armor Piercing rounds do bonus damage to armor. Warp Ammo is a close second if you have access to nether.
The weak points on a Harvester are the glowing disc in it's chest, or the eyes on the face. 3-4 shots from an Anti-Material rifle running Incinerary or Armor Piercing rounds here will put it down quickly.
If you're looking for a quick solution, take a look around the area briefly, most of the time there's a Hydra Rocket launcher or other heavy weapon nearby. One good bodyshot with the heavy weapon takes out that foe immediately.
The only place that this isn't fesable is the Thessia Mission. Just bunker down until Talon 5 returns to draw off the Harvesters. Between them and the Ravagers, pressing on is suicide.