This is probably your best bet

Expanded Tudor · More Info

Door canopy or bracketed entry roof · More Info

An entry like this would have columns that would impede movement on the porch

Crisp Architects · More Info

Or you could do this

Hornstein Residence · More Info

An awning type is the easiest but you have lots of space above the door for a proper amount of protection for guests like even a gable type cover

The issue will be the roof line and the not centered door so something custom for sure if going more than an awning, Lisedv has the right idea but a big heavy looking . I am curious why the dack was not taken all the way across .

Will suggest that you turn part of the deck into a porch. Any roof you add above the door is really going to just look stuck on.