One basic rule (or perhaps "convention" might be a better word) for determining romanized spellings, is whether two identical vowel sounds -- such as i + i, or u + u, belong to the same morphophonemic unit. In more common parlance, whether the two sounds belong to the same root or stem.
For adjectives that end in two i sounds, the last i is usually the conjugating portion -- this is the i that changes to ku in the adverbial form, like すず[し]{●}[い]{●} as an adjective changes to すず[し]{●}[く]{●} as an adverb. Since the final i belongs to a separate functional piece of the word, romanization practices generally keep this separate -- so すずしい = suzushii with the two i's spelled separately.
Likewise, みずうみ "lake" derives from 水 + 海, and the two u sounds belong to different roots. So this is similarly spelled spearately -- みずうみ = mizuumi with the two u's spelled separately.
However, in おにいさん, the two i's are part of the same root. Some romanization systems spell this as onīsan as a result. Likewise with borrowed terms like コーヒー: the two i's are part of the same root, and these are thus generally spelled together as ī as a result.
Other romanization systems spell *all* double-i's separately, sometimes out of a stated concern that the macron (the long bar) over the ī is too hard to distinguish visually from the tittle (dot) over the regular i.
There are multiple systems for romanizing Japanese, as Virmaior points to in his comment. Some of the main ones are Kunrei-shiki in Japan, and Hepburn, which is commonly used in English-language materials about Japanese. More at the Wikipedia article on Romanization of Japanese.