Paul's prayers seem to primarily aim for God, although as ever, Jesus is never far removed from view. In Romans 1, the prayer is even offered "through" Jesus. However, as Hurtado rightly notes, there are other occasions when both are addressed, such as 1 Thessalonians 3:11-13:
Now may our God and Father himself and our Lord Jesus clear the way for us to come to you. May the Lord make your love increase and overflow for each other and for everyone else, just as ours does for you. May he strengthen your hearts so that you will be blameless and holy in the presence of our God and Father when our Lord Jesus comes with all his holy ones.
There are also petition moments that include Jesus, such as Paul's famous petition to the Lord Jesus for the removal of his "thorn" in 2 Corinthians 12. Fascinatingly, Hurtado also informs us that in the "unsuccessful mutations" of Christianity, direct prayers to Jesus are actually more prominent than in the canonical material, which seems to keep something of a balance. Hurtado concludes:
Overall, we get the impression of a remarkably well-established pattern of prayer in which Jesus features very prominently, either as recipient or as unique agent through whom prayer is offered. Moreover, there is simply no analogy in Roman-era Jewish groups for the characteristic linking of Jesus with God in the prayer practice reflected in Paul's letters. (p. 140)