(Zn,Mg,Cd)Se quaternary alloys lattice matched to InP, a novel material for the fabrication of light emitting devices with light emission spanning the visible range, are difficult to dope p-type while their n-type doping is relatively easy. To address this issue, the p-type doping of the Zn1-xMgxSe and Zn1-yCdySe ternaries was investigated as a function of composition using a radio frequency discharge nitrogen plasma source. Besides conventional (uniform) doping, a type of delta doping that involves codoping with N and Te [(N + Te)delta doping] was performed. The p-type: doping level was increased by the (N + Te)delta doping, however, the net acceptor concentration (N-A-N-D) of both ternaries decreased with the addition of either Mg or Cd, indicating that both Mg and Cd atoms hinder the p-type doping of the alloys. To overcome these doping difficulties, we propose the growth of a Zn1 - x' -y'Mgx'Cdy'Se/ZnSe:N superlattice structure, in which the p-type doping is selectively performed only in the ZnSe region, as a substitute for the quaternary alloy.