Driving an infrared LED from a coin cell
This should work: -



Rset and Vset determine the current that flows through the load resistor: -

\$I_{LOAD} = \dfrac{V_{SET}}{R_{SET}}\$

However, the op-amp needs to be able to work down to 1.8 volts or lower and will need power connections (not shown above) to V and ground. It also must have rail-to-rail inputs and also preferably outputs.

If Vset is made to be 0.15 volts and Iset is required to be 15mA then Rset is 10 ohms.