Assuming you have a simple current mirror you should start with two things:
1. Keep the Veff in a reasonable range. This sets the transistor region and you want to be in saturation to achieve good matching and high immunity to variations.
2. Keep the Vds the same for the diode and the output transistor. What do you expect at the drain of the output transistor? If you expect a fixed 1 V make sure the diode has 1 V on the drain as well.
If you have a varying voltage on the output, the output voltage is very low etc. You have to look in to more advanced current mirror topologies.
Also check how sensitive you really are to changes in the output current, does it really have to be super accurate?