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In the Genki I textbook, it says that the i and the u vowels are sometimes
dropped when placed between voiceless consonants or at the end of an utterance
preceded by voiceless consonants.

The example given, すきです, demonstrates both points.

Currently, I am learning about adjectives and was wondering whether the vowel
drop is also applied to adjectives (or words in general) that end in "いい", for
example かわいい and うれしい.

Since the i is at the end of an utterance preceded by voiceless consonants in
both examples, I believe that the vowel drop is acceptable. Therefore, is it
appropriate in speech to say "kawaides" and "ureshides" or do I have to say
the long i-vowel?
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2016-07-18T19:24:59.987
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pronunciation contractions i-adjectives vowels long-vowels
Can the last い in かわいい be dropped?
The vowels aren't "dropped"; they simply become voiceless, which is explained
(poorly) to English speakers as being "dropped" because the concept of
voiceless vowels doesn't exist in English. In these two examples, the い is
voiced in both cases.

For かわいい, the voicing of わ means that the first い is voiced, and thus the
adjacent final い must also be voiced. Aside from that, though, if it's
followed by です then it doesn't matter since the [d] at the start is always
voiced. Thus the final い in うれしい must also be voiced. But since vowels are
voiced by default, the final い would also make the previous い voiced.
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2016-07-18T20:49:17.233
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answer
The vowel drop described in your textbook happens between consonants. However,
even though the vowel is dropped, the rhythm of the word isn't changed.

> [[s.ki.de.s]] ↔ [[su.ki.de.su]]

(the dot `.` denotes separation of syllables).

You cannot do the same with the [[i]] in かわいいです [[ka.wa.i.i.de.s(u)]] or
うれしいです. (I don't understand your comment about voiceless consonants, but
neither [[i]] is between consonants.)

* * *

However, a final -i is sometimes dropped in colloquial speech. I would
describe this as a separate phenomenon, though.

> 痛い → 痛っ or 痛ッ  
>  寒い → 寒っ or 寒ッ

In writing (e.g. ads, manga), the silent mora is usually represented by っ (or
ッ).

For your two words, you'd get

> カワイい → カワいっ  
>  うれしい → うれしっ

The second be pronounced [[u.ɺe.ɕ. ]], i.e. with a(n almost?) silent final -i.
However, note that the rhythm is not ~~[[u.ɺeɕ]]~~.
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