The child cancer, neuroblastoma (NB), is characterised by a low incidence of mutations and strong oncogenic embryonal driver signals. Many new targeted epigenetic modifier drugs have failed in human trials as monotherapy. We performed a high-throughput, combination chromatin-modifier drug screen against NB cells. We screened 13 drug candidates in 78 unique combinations. We found that the combination of two histone methyltransferase (HMT) inhibitors: GSK343, targeting EZH2, and SGC0946, targeting DOT1L, demonstrated the strongest synergy across 8 NB cell lines, with low normal fibroblast toxicity. High mRNA expression of both EZH2 and DOT1L in NB tumour samples correlated with the poorest patient survival. Combination HMT inhibitor treatment caused activation of ATF4-mediated endoplasmic reticulum (ER) stress responses. In addition, glutathione and several amino acids were depleted by HMT inhibitor combination on mass spectrometry analysis. The combination of SGC0946 and GSK343 reduced tumour growth in comparison to single agents. Our results support further investigation of HMT inhibitor combinations as a therapeutic approach in NB.