'Sobering' is a less colorful and more polite word to capture the effect.

“Buzzkill” isn’t bad or rude at all. It is very casual, though.

A "wet blanket." For example, "I don't want to invite him to the party because he is always such a wet blanket." (He is not fun, and he ruins the good mood.) Good luck!

There's nothing especially rude about "buzzkill", but just keep in mind that it's slang, and so shouldn't be used in any kind of formal context. I can't think of a more formal word that means the same thing exactly, but for example, if you took the sentence, "That guy is such a buzzkill." You could say it without slang saying, "That guy always ruins our fun." or "That guy always dampens the mood." And yes, you can use "downer" as a synonym. It's also slang, and you don't need to use "Debbie". Example: "Don't be such a downer."

A newer expression meaning the same is "Debbie Downer". You can find old Saturday Night Live sketches with their Debbie Downer character to illustrate this concept.