Funny enough, I've stopped having problems with the pizza delivery service since the major patch they released right before C&D this fall.
It takes my poor pc a bit of time to materialize the maid or other service NPCs. I am running on an older pc and am only meeting base game requirements, which makes the game really interesting at times. I was having problems with the Maid, Repairman, and Pizzaman showing up, and I discovered with Service NPCs I have to pause my game for them to actually appear on time. If I want my maid to show up right after 10am (when she's supposed to), I pause my game at that sim-time and poof, she appears after some hardcore processing from my tired computer. If I didn't hit pause she wouldn't show up at all, or show up around 3-4pm. Same with the repairman and pizza, if I don't see the deliveryman in a sim hour, I'll pause, the game will catch up, and he'll usually appear with pizza. I'm not sure what kind of pc you're running the game on, so this might not help, but I'd thought I'd throw it out there.