AFAIK the conversion would be almost useless and you may end up with a messed up braking system even worse than the stock one.
As you hit the brake the car tends to push all its weight at the front, so front brakes do all the hard work, rear ones only share some 10-20% brake force. Your stock drum brakes were designed to do this in the best possible way. Installing an aftermarket disc arrangement won't do better than the stock balanced system.
If you want to get better brakes do get bigger booster, bigger discs and multi piston brake caliper installed in the front. Or you can simply put better tyres for better brakes. You may also install harder suspension for better brakes and handling.
Still, if all you need is 4 discs, you can get a bolt-on system from European Civic, the original one on which your City is based on. The top model of that Civic even came with B18 engine + LSD gear, 4 wheels disc + antilock + traction control. Everything from that car would just fit easily in your City.
Best of luck. Cheers