What I was taught ages ago, and what seems to be borne out by the things I've read and pored over through the years, modern katakana uses the 長音符【ちょうおんぷ】 (literally, "long sound mark") or 伸【の】ばし ("lengthener") to indicate long vowels. In horizontal text, this looks a bit like an em dash or even an ichi kanji 一, while in vertical text, it's a vertical line that is clearly distinct from a horizontal hyphen or ichi.
That said, there are special cases even in modern use where you might see something romanized as kō spelled in katakana as コウ, particularly certain dictionary publications that use katakana to spell out the on'yomi for kanji. And historically, starting (I think) from probably some time in the Meiji or Taishō eras and up until World War II, katakana was the standard kana form for regular official published texts -- not hiragana.
So in any modern context, for words like kōto, you will almost always see コート. You might rarely encounter コオト, but that's because the author is trying to be cute or stylistically distinct somehow, kinda like English nite. -- the "regular" way to spell it is with the 長音符. I don't think you'll ever see コウト, since this is a borrowed word that has never had an "u". (On'yomi with o + u in kana are pronounced nowadays as one long ō, but historically, these did actually have that u sound.)