If you are SURE that voltage is to be kept at about 3.1 V for all the charging process, simply let the battery to sink the current it needs. In fact you can not control both voltage and current simultaneously.
However some batteries (for example NiCd)need to be charged at a constant current, and when they reach a specified voltage level, they must be disconnected (current= 0).

Maybe you can get some info from battery manufacturers.

Alfredo.