Supervised learning is often used to count objects in images, but for counting small, densely located objects, the required image annotations are burdensome to collect. Counting plant organs for image-based plant phenotyping falls within this category. Object counting in plant images is further challenged by having plant image datasets with significant domain shift due to different experimental conditions, e.g. applying an annotated dataset of indoor plant images for use on outdoor images, or on a different plant species. In this paper, we propose a domain-adversarial learning approach for domain adaptation of density map estimation for the purposes of object counting. The approach does not assume perfectly aligned distributions between the source and target datasets, which makes it more broadly applicable within general object counting and plant organ counting tasks. Evaluation on two diverse object counting tasks (wheat spikelets, leaves) demonstrates consistent performance on the target datasets across different classes of domain shift: from indoor-to-outdoor images and from species-to-species adaptation.