I didn't eat my children's placentas (hospital births), but a friend of mine did.
For the first two pregnancies, she didn't, but after serious post-partum with both (she referred to it as the "galloping heebie-jeebies") she decided to give it a try. She went of to have five more children, and no more post-partum, so pretty nice anecdotal evidence in favour of ingesting the placenta.
Her method was to cook and eat it. She'd been advised that the flavour was very much like liver (which it was), and so she simmered with onion, garlic, and a little worcestershire sauce, and ate it on a bed of potatoes or brown rice.
In general, supplements are very useful to people that are lacking in that particular item, and pass through those who already had a sufficient amount. It sounds like a good idea - the worst it can do is nothing, and it just might be the boost you need.
(p.s. Slightly ranging from topic, but other non-chemical mood-boosters include breast-feeding, valerian root, and sunlight. I battle chronic mild depression myself - for me, the year of breast-feeding after each pregnancy was definitely helpful, despite many stressful events during those times.)
Carrie