The switch needs to apply at least -9 volts to pin 12 with the return being pin 1. Driving the coil directly from a switch may or may not work well because switch bounce might toggle the relay more than once as it closes and opens. The required coil pulse width is >10 ms and the rise time is described as "fast."
The circuit above will debounce the switch with an attack time of about 2 ms and a debounce time of about 50 ms. The capacitor can be a 33 uF electrolytic, tantalum, or ceramic with a voltage rating of 15 volts or more.
Note that on page 3 of the datasheet the diagrams for the Single coil and the Dual coil are switched (they are in the wrong place).
Unless they fixed the pdf, the diagrams look right to me. The double latch set coil is between pins 1 and 12 and the reset coil is between pins 5 and 7. The single latch uses a single coil for both reset and set between pins 1 and 12 thus relying on polarity of the signal/pulse on the pins. Your circuit will set it, reset is not shown. On using the capacitor in place of a diode, the diode will impart opposite polarity to a polarized cap - will that matter since it's only briefly?
You're right! The diagrams are correct, and to operate the single coil latch type a circuit with these characteristics is needed:
Do we want the relay to power-up in the last state it was in or should it have a power-up reset to a specific state?
It will work like so: