The results of a comprehensive positronium annihilation study of the phase behaviour of carbon dioxide in porous Vycor glass are presented. Isobaric measurements of the 3 gamma:2 gamma annihilation ratio show that on cooling, the gas-liquid phase boundary is raised by similar to 5 K while the liquid-solid transition is depressed by similar to 12 K relative to the bulk. The resulting phase diagram suggests the existence of a 'triple point' of the confined fluid at a temperature similar to 10 K and a pressure similar to 2 bar below the bulk triple point.