OK I tried:
Diodes on base: 2 x 1N4148
Resistor on base: 330 Ohm
Resistor on emitter: 10 Ohm
This setup give a collector current almost independent of the suply voltage:
Supply Voltage /Collector current
3.8V 78 mA
7,6V 89 mA
11,4V 91 mA
The base current is 9,5 mA