Deep stochastic configuration networks (DeepSCNs), as a kind of randomized learner model, have the capability to generate a learning representation quickly and efficiently. Based on DeepSCNs, convolutional stochastic configuration networks (ConSCNs) demonstrated superiority in spectroscopic data analytics by utilizing 1D convolutional and pooling operations. However, directly employing 1D ConSCNs in image data analytics could potentially lead to the loss of spatial information in images and poor generalization performance. This paper extends the original ConSCNs to a 2D version, termed 2DConSCNs, aiming at rapidly constructing randomized learners with 2D input shapes. Empirical results on eight benchmark datasets demonstrate the proposed 2DConSCNs outperform several existing randomized learner models and show good potential for image data analytics.