Use DALI interface to power the device
You need diodes to charge up a capacitor from the DALI line when the voltage is high, so it will stay charged when the voltage goes low for short periods. It should be designed to work continuously at the lowest high voltage of 9.5V, but bear in mind that as the traffic increases, the average line voltage tends towards half of that. It won't quite reach half because during the stop condition and minimum interpacket spacing periods the line is at high level.

Also make sure your transmit transistor is on the DALI line side of the diode so that you are not shorting out your own power supply line directly when you transmit but are using the charged capacitor. Making the capacitor too big can be a problem because it will draw a surge current when the device is attached, one solution is to restrict the charging rate.