Theres a car park over at the Custom House, beside the Waterfront Leisure complex, its a really big parking area for the shops like Comet, Currys etc.
I would imagine it should be safe enough, I'm sure there is plenty of CCTV around. Or across the road from Tesco, there is an entrance to a carpark, and it takes you to the Greenock Town Hall, there is a little parking area in there im sure is open to general parking all the time.
Anywhere in the Town Center is close enough to walk to the harbor anyway, only a 5 minute walk away!