Short-and-sweet; I've been working on a multi-part serialized Rock Opera similar to Coheed & Cambria's Armory Wars in concept, but not in the plot. Sadly, whenever I write lyrics for anything in it, which I want to, as I enjoy singing as well as playing, it comes out as incredibly corny and silly. How do I write a rock opera lyrics that can actually be taken seriously?

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make sure your telling a story with a fantastic plot. like rush's 2112.

"see how it sings like a sad heart, and joyously screams out its pain
notes that build high like mountains, or notes that fall gently like rain"

those are corny as shit but it works incredibly well because(for me) it describes how i feel about guitar perfectly
There's nothing wrong with being literal in songs. In fact, I try rather hard not to use a lot of metaphors, because they're easy. Just tell a story, plain and simple.
I was thinking the same... determine what the song is about. Develop your idea(s) for each verse/chorus without thinking about rhymes. Once you have the basic concept of each section for the song, and what needs to be said, then you work each section accordingly. Good lyrics require constant work... followed by sleep... waking the next day and checking over your work, etc. Trying to rush it often results in the corniness.
Just listen to a bunch of rock opera/progressive concept albums. The lyrics to Scenes from a Memory by Dream Theater have always been favorites of mine, but also check out 2112 by Rush and even De-loused in the Comatorium by The Mars Volta. They all have very different styles of telling a story, some abstract and some very literal. It's up to you to decide which style or mix of styles to use in composition. Have fun!
To caveat off what I said earlier. Check out the album "Pizza Deliverance" by the Drive By Truckers. It's a concept album that just tells a story, without heady themes or breat big braniac overtones. It could very easily be a musical.
listen to songs from the black hole by rivers cuomo/weezer. the main story itself is really simple and not extremely unique, but the relationships and interactions between the characters that he creates are actually really good. its an actually believable story.

i would definitely work on writing a whole story though, whether in book form or as a script, and then take ideas and events that go together in the story and have them be the individual songs. from there you just have to explain the story musically and lyrically , which is the tricky part.