Yes they did! Note that for this response I will be ignoring ancient Berber scripts and focusing on scripts used after the Arabization of the Maghreb. I will also be focusing on Morocco as I feel unqualified to answer with regards to the rest of the region.

Berber speakers from the Middle Ages through to the present day wrote in the Arabic script. This is formally known as the Berber Arabic alphabet and has been used alongside the Berber Latin alphabet which appears after the 19th century. Special letters were added to both scripts to represent phenomenons not typically found in either alphabets.

In the 20th century the Neo-Tifinagh script was adopted by Tamazight speaking peoples in Morocco, a descendant of the Tifinagh and ancient Berber alphabets. However, Berber languages were repressed and using the script could lead to imprisonment in the 1980's and 1990's. Throughout this time; signs written in Tifinagh were taken down by the government

Thus, activists and Berber speakers have historically favoured the Latin alphabet over Tifinagh. The Latin alphabet was introduced through French colonialism in North Africa. According to Souag, the French tried to Romanise both Arabic and Berber dialects however as Berber did not have much of a modern literary tradition in it's own script it was receptive to these schemes.

In 2003 the King of Morocco signed a law declaring that the Tifinagh script was the official script for the Tamazight language. From the 1st of July 2011 onward; Berber has been an official language in Morocco, the Royal Institute of Amazigh Culture has solely regulated the Tamazight language in Morocco since then. The decision to include Tamazight as an official language followed the 2011 constitutional referendum in Morocco.

Sources:

Writing Berber Languages: a quick summary, Lameen Souag

Graphèmes berbères et dilemme de diffusion, Aghali-Zakara

Report on the ordeal of writing Tifinagh in Morocco, Hassan Idbalkassm