When is a CFII required to provide instrument training?
No, you cannot provide


  instrument training for the issuance of an instrument rating, a type rating not limited to VFR, or the instrument training required for commercial pilot and airline transport pilot certificates


Unless you hold


  (1) Except as provided in paragraph (c)(2) of this section, the flight instructor must hold an instrument rating appropriate to the aircraft used for the instrument training on his or her flight instructor certificate,


Having an instrument rating on your CFI makes you a CFII.

You are confusing a CFII, who is a CFI with an instrument rating on his / her flight instructor certificate, with

someone that has an instrument rating on his / her pilot certificate and who also might hold their CFI.

You must be a CFII to give instrument training, the exception to that would be for private pilot candidates from 61.109


  (3) 3 hours of flight training in a single-engine airplane on the control and maneuvering of an airplane solely by reference to instruments, including straight and level flight, constant airspeed climbs and descents, turns to a heading, recovery from unusual flight attitudes, radio communications, and the use of navigation systems/facilities and radar services appropriate to instrument flight;


a CFI is able to give those 3 hours of instruction.  Anything beyond private pilot is the realm of the CFII.