You possibly don't know it, but there are semiconductor devices designated "current limiter diodes", e.g. former Siliconix CRxxx, Microsemi 1N52xx series. They are basically JFETs with internal source resistor, well suited as true two-pole current source. Unlike a current mirror, they source fairly constant current also with varying voltage.
At a higher current level above several mA, adjustable voltage regulators as LM317 can be used as two-pole current source. More complex circuits can work at any current level and also meet higher accuracy requirements.
FvM is very correct. However, these diodes which I have used, are not all that precise. If you want precision you will have to use a bandgap reference in an op amp circuit.