He's feeding 220V into the timer. I would imagine(!) that 220 in can't give you 110 out.
Another option is to modify the timer such that the built-in relay switches a separate 110V supply. So the timer would have 2 power cords; the existing 220V for the timer itself and an additional 110V for the timer's enlarger relay switching contacts, not the solenoid. But it gets a bit messy that way and a mistake is easily made. Therefore I wouldn't recommend that route.
Voltage converters are fairly cheap, check out these guys, they're in Montreal as well. But first see if the timer's internal power supply can be set to 110V.
I misinterpreted the OP. But yes, it's stepping up not down. DOH!