Massive black hole binaries at sub-parsec separations may display in their spectra anomalously small flux ratios between the MgII and CIV broad emission lines , i.e . F _ { MgII } / F _ { CIV } \mathrel { \hbox to 0.0 pt { \lower 3.0 pt \hbox { $ \sim$ } } % \raise 2.0 pt \hbox { $ < $ } } 0.1 , due to the erosion of the broad line region around the active , secondary black hole , by the tidal field of the primary . In Paper I by Montuori et al . ( 2011 ) , we focussed on broad lines emitted by gas bound to the lighter accreting member of a binary when the binary is at the center of a hollow density region ( the gap ) inside a circum-binary disc . The main aim of this new study is at exploring the potential contribution to the broad line emission by the circum-binary disc and by gaseous streams flowing toward the black hole through the gap . We carry out a post-process analysis of data extracted from a SPH simulation of a circum-binary disc around a black hole binary . Our main result is that the MgII to CIV flux ratio can be reduced to \sim 0.1 within an interval of sub-pc binary separations of the order of a \sim ( 0.01 - 0.2 ) ( f _ { Edd } / 0.1 ) ^ { 1 / 2 } pc corresponding to orbital periods of \sim ( 20 - 200 ) ( f _ { Edd } / 0.1 ) ^ { 3 / 4 } years for a secondary BH mass in the range M _ { 2 } \sim 10 ^ { 7 } -10 ^ { 9 } { M _ { \odot } } and a binary mass ratio of 0.3 . At even closer separations this ratio returns to increase to values that are indistinguishable from the case of a single AGN ( typically F _ { MgII } / F _ { CIV } \sim 0.3 - 0.4 ) because of the contribution to the MgII line from gas in the circum-binary disc .