From CNA: 

A bishop has authorized and published a prayer for private devotion to Pope Benedict XVI, who died Dec. 31, 2022, at the age of 95 in Rome.

Bishop Carlos Rossi Keller of the Diocese of Frederico Westphalen in the Brazilian state of Rio Grande do Sul published the prayer in Portuguese, Spanish, French, and Italian.

The prayer:

Eternal and Almighty God,
who inspired in the heart of your servant Pope Benedict XVI
the sincere desire to encounter you and announce you,
becoming a humble “co-operator with the truth”
and offering himself as a servant,
for Christ and for the Church,
make me also know how to love the Church of Christ
and to be able to follow in my life the eternal truths that she proclaims.
Deign, Lord, to glorify your servant, Pope Benedict XVI,
and grant, through his intercession, the favor I now ask of you (mention your petition). Amen.

Pray an Our Father, Hail Mary, and Glory Be.