The lamp appears to have 9 LEDs in it, and white LEDs generally have a forward voltage drop of about 3.5 volts, so it appears they've arranged the LEDs as 3 paralleled strings of 3 LEDs connected in series, which would account for the 9-12 volt range in forward voltage.
If they're rated for a forward current of 1 ampere, then the best thing to do would be to connect the 5 lamps in series and drive them with a 1 ampere constant current source with a compliance greater than 60 volts, like this:
That'll allow the voltage drop across each lamp to become unimportant since the supply will only allow 1 ampere through the lamps.
One caveat is that if one (or more) of the lamps has a forward voltage of 12 volts and there's 1 ampere through it, it'll be dissipating 12 watts, not 10, so to stay within the 10 watt limit your power supply should be adjusted to 830 milliamperes.
Most important: You'll need to provide some heavy-duty heatsinking for the lamps.