The seriousness of Libation Bearers is pretty obvious and runs straight through the play. The only possible exception to its generally weighty tone comes in the Nurse's speech, when she talks about how Orestes used to pee himself a lot when he was a kid. If that isn't intended as comic relief, we don't know what it is.
What about hopeful? Well, this has to do with an interesting contrast between Libation Bearers and Agamemnon, the first play of the Oresteia trilogy. If you've read Agamemnon, you may remember that the entire play has this serious undercurrent of dread. Most of the characters have a general sense of eeriness, they just don't know what it is. At the end, when the murder happens, it's like the moment when the Jaws shark finally attacks after a whole movie filled with creepy music, gruesome deaths, but no shark.
Libation Bearers is a little bit different in tone from Agamemnon. In Libation Bearers, we are on the side of the people plotting the murder: Orestes, Pylades, Electra, and the Chorus (even the Nurse counts, to a certain extent – though she's more of an unwitting accomplice). From their perspective, the killing is a good thing; they're hoping for it to happen, and they're afraid that it won't happen. (Interesting, huh?) The tone is dark because the end of the play shows us that even what most of the characters hoped for – the killing of Aegisthus and Clytemnestra – is a horrible thing. Orestes's madness at the end is truly terrifying, and definitely a dark note to end on.