I will say something a long the lines of 暇だ for I am bored and つまらない（名刺） for something is boring. However, when my Japanese friends spit it back out in English they don't seem to understand the nuance. How can I properly convey this?
I had the same issue with awkward in Japanese earlier ~_~.
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暇だ for I am bored
暇だ doesn't mean "I'm bored". It means "I'm not busy".
As far as I know, there is no clear way to express the concept of "I am bored" in Japanese where "bored" is a Japanese word for the human emotion of wanting something to do.
You would have to say, つまんないな, which literally means, "(something/this/that) is boring" or 何かしたいな--"I want to do something" or 退屈だな "(something/this/that) is in a state of boringness".
However, wikipedia does tell me that 退屈 can mean "the emotion of boredom", but I've never heard it used as such. Never used like 僕の感情は退屈だ, but always used like この状況は退屈だ. But maybe some native speaker could comment on this exact usage.
Rephrase it so that you don't need to describe "boredom" as a human emotion.
暇 is often translated as "bored" because there are a lot of situations in which that is what it implies. 「暇でしょうがない」 could be translated as "Darn, I'm just so not busy that it sucks", but what it means is, "I have nothing to do, I'm really bored."
As for 退屈... if we look at the kanji, we can see that it's composed of 退 and 屈. They can be considered to have the meanings of "withdraw" and "capitulation". To say that something is 退屈 is to say that it is something that you (or your interests, or something to that effect) are likely to withdraw from, and to give up. If we look at the etymology of 退屈, we can see that it is just so.
I think in modern Japanese, 退屈だ can describe the state of "being bored", but I believe that it is more commonly interpreted as describing something as boring. However, in its verb form, 退屈する does not describe something as "being boring", but rather something "being bored". 子供が退屈している doesn't mean that the children are being boring, but rather that they are bored.
With this in mind, I believe that the best way to interpret 退屈, as an adjective, is to say that it means "such that it causes boredom".
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I want to say that the closest we'll get to the English word "bored" is 退屈している. Not that it should be the go-to word for OP, but it does seem describe the state of "wanting something to do", or at least "having become disinterested with the current state of things".