Spoken language recognition (SLR) is the task of automatically identifying the language present in a speech signal. Existing SLR models are either too computationally expensive or too large to run effectively on devices with limited resources. For real-world deployment, a model should also gracefully handle unseen languages outside of the target language set, yet prior work has focused on closed-set classification where all input languages are known a priori. In this paper we address these two limitations: we explore efficient model architectures for SLR based on convolutional networks, and propose a multilabel training strategy to handle non-target languages at inference time. Using the VoxLingua107 dataset, we show that our models obtain competitive results while being orders of magnitude smaller and faster than current state-of-the-art methods, and that our multilabel strategy is more robust to unseen non-target languages compared to multiclass classification.