Can I use sunflower oil to make pesto?
I see no problem with your plans. You will - obviously - get a somewhat different taste, depending on which type of sunflower oil you use.


For the refined, basically tasteless oil, the pesto might be a bit blander and the taste of your other ingredients more pronounced. 
If you are using a cold-pressed unfiltered oil, you'll get the nutty undertones of the sunflower seeds, which will work well with a classic basil / pine nut / parmesan type of pesto.


Note that many commercially sold pesto jars use only a small amout of genuine olive oil and often also skimp on the pine nuts, cheaper neutral oils and sunflower seeds are a frequent stand-in. So you should be absolutely fine.