
This subject, I feel, doesn't get enough attention and yet I think it's a fascinating topic: African loanwords in the Etruscan language. Considering what little Etruscanists currently seem to know about the language, unable even to explain conjugation and declension as I have attempted on this blog, it's probably unrealistic to expect that I should find a published mention of Punic or Berber adstrate in Etruscan, and yet, surely some African loans wandered their way into the vocabulary of ancient Italy, no?
The relationship of Etruria with Carthage is well proved ever since the Pyrgi Tablets were discovered. These are bilingual artifacts written in Etruscan and Punic. Punic, a dialect of Phoenician, was the official language of Ancient Carthage in what is now Tunisia. Berber dialects must also have been spoken in the Carthaginian region but Berber is a separate although related group to the Semitic and Egyptian languages traditionally to the east.
There is at least one word that may be considered Berber, at least based on the popular etymologies of the name Africa which source it either to afar 'dust' or to ifri 'cave, cavern' in allusion to local cave-dwelling. The name Afircina is recorded in ET AT 3.2 in the form of the type-I dative Avhircinasi 'to/for Afircina'. This mirrors Greek Ἀφρική 'Carthaginian region' and Latin Āfrica 'Carthaginian region'.
Now what about other African words, hmm? So far I've spied my eye on Proto-Berber *a-kal[1] which bears a curious resemblance to Old Etruscan cal(u) 'earth', attested by calus 'of the earth' [TCap xv] and calusi-m 'and to the earth' [TLE 99]. Later, Etruscan a regularly rose to e before resonants like l. It should be noted that in Berber languages, noun stems are completed by additional gender prefixes like masculine singular *a- and feminine singular *ta-, so there's an unusual wealth of nouns with vowel onsets in their citation form.
Coincidentally Phoenix has been exploring the Berber language in great depth on his blog and I've been reading it avidly to guide me through this oft-neglected but fascinating and historically important language group.

NOTES
[1] Phoenix in a comment below justifies Proto-Berber *a-ʔkal instead.