This paper investigates data augmentation for deep neural network acoustic modeling based on label-preserving transformations to deal with data sparsity. Two data augmentation approaches, vocal tract length perturbation (VTLP) and stochastic feature mapping (SFM), are investigated for both deep neural networks (DNNs) and convolutional neural networks (CNNs). The approaches are focused on increasing speaker and speech variations of the limited training data such that the acoustic models trained with the augmented data are more robust to such variations. In addition, a two-stage data augmentation scheme based on a stacked architecture is proposed to combine VTLP and SFM as complementary approaches. Experiments are conducted on Assamese and Haitian Creole, two development languages of the IARPA Babel program, and improved performance on automatic speech recognition (ASR) and keyword search (KWS) is reported.