There is a small difference between the people and the tree:
Indicating long vowels with a bar and short ones with a cup as usual, the masculine word is pŏpŭlŭs and the feminine one pōpŭlŭs.
Long vowels are indicated in many dictionaries, whereas short vowels are indicated by a lack of macron (the bar).
Vowel lengths are typically not marked in writing, but you might want to do so to make the distinction.
If you write vox pōpuli, it is clear that you mean the tree.
(The O in vox and the final I are also long, but those lengths need no emphasis. You can use macrons for all long vowels or only when emphasis is needed.)
If in the same text you also want to refer to the voice of the people, you might want to emphasize the shortness: vox pŏpuli.
To emphasize ambiguity, you could write vox pō̆puli.
As suggested in comments below, you could use the phrases in a metric verse to indicate vowel length.
The rhythm typically unambiguously determines whether the O is long or short.
Inspired by this idea, I composed this hexameter verse:
Vox populi statuit sic nunc: vox populi abesto!
The voice of the people has decided this now: the poplar shall have no voice!
The simplest way, however, is to use an adjective which indicates the gender.
Vox populi Romani is the voice of the people of Rome, but vox populi Romanae is the voice of the Roman poplar.
However, this distinction will only work for adjectives of declension 1/2 and fail in the third declension.