Starting from the classical r-matrix of the non-standard (or Jordanian) quantum deformation of the sl(2,R) algebra, new triangular quantum deformations for the real Lie algebras so(2, 2), so(3, 1) and iso(2, 1) are simultaneously constructed by using a graded contraction scheme; these are realized as deformations of conformal algebras of (1 + 1)-dimensional spacetimes. Timetype and space-type q...