The unique behavior of colloids at liquid interfaces provides exciting opportunities for engineering the assembly of colloidal particles into functional materials. The deformable nature of fluid-fluid interfaces means that we can use the interfacial curvature, in addition to particle properties, to direct self-assembly. To this end, we use a finite element method (Surface Evolver) to study the self-assembly of rod-shaped particles adsorbed at a simple curved fluid-fluid interface formed by a sessile liquid drop with cylindrical geometry. Specifically, we study the self-assembly of single and multiple rods as a function of drop curvature and particle properties such as shape (ellipsoid, cylinder, and spherocylinder), contact angle, aspect ratio, and chemical heterogeneity (homogeneous and triblock patchy). We find that the curved interface allows us to effectively control the orientation of the rods, allowing us to achieve parallel, perpendicular, or novel obliquely orientations with respect to the cylindrical drop. In addition, by tuning particle properties to achieve parallel alignment of the rods, we show that the cylindrical drop geometry favors tip-to-tip assembly of the rods, not just for cylinders, but also for ellipsoids and triblock patchy rods. Finally, for triblock patchy rods with larger contact line undulations, we can achieve strong spatial confinement of the rods transverse to the cylindrical drop due to the capillary repulsion between the contact line undulations of the particle and the pinned contact lines of the sessile drop. Our capillary assembly method allows us to manipulate the configuration of single and multiple rod-like particles and therefore offers a facile strategy for organizing such particles into useful functional materials.