Finding and classifying astronomical sources is key in the scientific exploitation of radio surveys. Source-finding usually involves identifying the parts of an image belonging to an astronomical source, against some estimated background. This can be problematic in the radio regime, owing to the presence of correlated noise, which can interfere with the signal from the source. In the current work, we present ConvoSource, a novel method based on a deep learning technique, to identify the positions of radio sources, and compare the results to a Gaussian-fitting method. Since the deep learning approach allows the generation of more training images, it should perform well in the source-finding task. We test the source-finding methods on artificial data created for the data challenge of the Square Kilometer Array (SKA). We investigate sources that are divided into three classes: star forming galaxies (SFGs) and two classes of active galactic nuclei (AGN). The artificial data are given at two different frequencies (560 MHz and 1400 MHz), three total integration times (8 h, 100 h, 1000 h), and three signal-to-noise ratios (SNRs) of 1, 2, and 5. At lower SNRs, ConvoSource tends to outperform a Gaussian-fitting approach in the recovery of SFGs and all sources, although at the lowest SNR of one, the better performance is likely due to chance matches. The Gaussian-fitting method performs better in the recovery of the AGN-type sources at lower SNRs. At a higher SNR, ConvoSource performs better on average in the recovery of AGN sources, whereas the Gaussian-fitting method performs better in the recovery of SFGs and all sources. ConvoSource usually performs better at shorter total integration times and detects more true positives and misses fewer sources compared to the Gaussian-fitting method / however, it detects more false positives.