All dogs can do this, I think - "The Look" which dog owners everywhere will recognise (and parents of small children, too, perhaps: mine performed much the same Look when they wanted something). It is in the angle of the neck and the tilt of the head which has to be just so - allowing for the pupils to be uplifted at a suitably beseeching angle.
To paint this, therefore, it is a question of carefully measuring the angles and getting them correct. Annoyingly, the brain, eye, hand movement can sometimes fail somewhere in the process: I found myself inadvertently straightening everything out. Which completely ruins "The Look", of course. So using a pencil (or whatever) - measure the angles. It is all in the angles.