[i-adj] + 限りだ [na-adj] + な + 限りだ [noun] + の + 限りだ
限りだ goes after a word for a feeling and says the feeling is as strong as it gets: "I couldn't be happier", "it's terribly sad". An い-adjective takes it directly, and a な-adjective takes な in between.
A few nouns of feeling take の instead: こうえい光栄のかぎり限り, "the greatest honour".
The adjective has to say how the speaker feels – glad, lonely, envious, grateful, ashamed. An adjective for a size, a price or a colour can't take 限りだ: ×大きい限りだ, ×高い限りだ. The feeling is also the speaker's own, so the sentence reports how you feel about something, not how someone else feels.
限りだ is stiff and states the feeling calmly, which is why it turns up in speeches, thank-you letters, apologies and formal writing. てたまらない says a feeling is too strong to hold back, and it is at home in conversation, as is a plain ほんとうに本当にうれしい嬉しい.