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I am learning Japanese, and need to enter romaji into my keyboard to enter
Japanese into documents and tables on my smartphone.

My textbook shows ī as the only romaji that can be spelled as a double ii.

[![romahi long
vowels](https://i.stack.imgur.com/kezUa.jpg)](https://i.stack.imgur.com/kezUa.jpg)

Is this a commonplace romaji writing convention, and if so, then why is this?

EDIT:

Would I be right in saying that it is because the alphabetical combinations いい
occur in Japanese (words), whereas ああ, うう, ええ, おお do not?
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kana kana-usage
Why ī is the only romaji that can be spelled as a double ii
There are several kinds of romanizations, each with its own set of rules.
Those rules were decided by whoever designed that romanization.  
So if you ask the reasons for a certain romanization... who knows? Probably
only the creator of that romanization knows the reason.

But I have a guess: I think ii is listed just because i and ī are too similar
and difficult to tell apart.  
So in order to avoid confusion they may use ii instead of ī.
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( Maybe someone said this in the comment already. )

I think it's because (the long vowel) いい appears in regular words, as --
かわいい、いいこと、いいます、（人名、地名： いいだ） . . .

( So if you romanize these, they'd be: kawaii, iikoto, iimasu, iida, ... )

Whereas ああ, うう, ええ, おお usually do not. Instead, they are usually written with
the bar (?) "ー" （長音記号） sign :

  * アーサー、ツアー、アームストロング、（嗚呼） 『あゝ玉杯に花うけて』

  * ウーロン茶、ウーパールーパー

  * エールフランス、エーデルワイス -- Exceptions where ええ is used : 「ええ話や…」

  * オープン、オーストリア、オート三輪

おお is used : おおかみ、オオカミ、オオクワガタ、… おおきな、おおらかな、おおしい、（人名、地名： おおき, etc.）

But "ee" and "oo" are avoided because they may be confusing : "feet" and
"food", etc.
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Hepburn originally transcribed `いい` as `ī`, but in later editions he changed
it to `ii`. Unfortunately, his book doesn't explain why he made this decision,
so I can't say with certainty what the reason was.

I think one reason is most obvious and likely, however: `ī` looks very similar
to `i`, and writing `ii` avoids confusing the two. This isn't a problem for
`a`, `u`, `e`, or `o` because they don't normally have dots over them, so
they're visually distinct from `ā`, `ū`, `ē`, `ō`.

Note that Hepburn did not make the distinction mentioned in Eiríkr Útlendi's
comment; he transcribed `いい` in all cases as `ii`. Although a few people do
make that distinction, it's not common to do so, and you don't have to worry
about it as a learner.

You wrote:

> Would I be right in saying that it is because the alphabetical combinations
> いい occur in Japanese (words), whereas ああ, うう, ええ, おお do not?

No. We can find all five kana sequences in Japanese words. The easiest
examples for the rest are interjections: `ああ`, `ううん`, `ええ`, and `おお`.
Interjections aside, `ああ` is also an adverb, and `おお` appears in a number of
words such as `おおい` and `おおげさ`. We can find more examples if we include
sequences that cross morpheme boundaries, such as `ええん` (会厭) and `ふうう` (風雨).

If you intended to include examples where a long vowel follows a consonant
(although these are technically excluded by what you wrote), we can find more
examples rather easily: `おかあさん`, `ずうずうしい`, `おねえさん`, and `ほのお`.

The explanation in your edit doesn't really make sense.
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the double ii was copied form european laguages ( romanian an italian).. as
this did not exist in Japanese languages before 19 century and japan look
towards europe for inspiration. It could also be that japan has strong
feelings towards(hawaii)
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