Bismillaah-ir-Rahmaan-ir-Raheem.

Assalaamu 'Alaikum wa Rahmatullaahi wa Barakaatuh.

May Allaah reward you for your earnest desire to follow the beautiful Sunnah of the Prophet (sallallaahu 'alayhi wa sallam).

In our knowledge, there is no specific dua to be recited in order to increase the growth of the beard.

However, you should not feel disheartened, as if you naturally do not grow one, or grow a very small one, you shall not be blameworthy. 'Abdullaah ibn Zubair (radhiallaahu anhu), a companion of the Messenger (sallallaahu 'alayhi wa sallam) naturally did not have a beard at all. (Al-Ikmaal Fi Asmaa-ir-Rijaal, pg. 604)

And Allaah knows best.

Wassalaam.