In these nine days leading up to the Solemnity of Pentecost, there are no set prayers as such. We are all just called to pray with expectation in the same way that the Apostles and Mary prayed in the upper room in Jerusalem.
We can offer Rosaries or read the Scriptures or any litanies of our own choice. We can also use the resources from the "Thy Kingdom Come" initiative which we can find on the Prayer Resources Page of this website.
alternatively here are some traditional prayers to the Holy Spirit which we will be praying after Mass each day.