Coke oven corbel structures include an assembly of multiple stacked tiers of refractory blocks defining a plurality of substantially vertically oriented central flues and a plurality of diagonally oriented lateral flues. At least one tier of refractory blocks in the assembly includes by an alternating plurality of saddle blocks and central diagonal flue blocks. The saddle blocks may include a laterally opposed pair of upright columns which define therebetween a rectangular channel, and a substantially vertically oriented cylindrical flue extending from a bottom surface of the saddle blocks to the rectangular channel thereof. The central diagonal flue blocks may include an arcuately concave flue channel defined between top and bottom surfaces thereof so that an upper opening to the flue channel at the top surface is inwardly offset relative to a lower opening thereof at the bottom surface.