The displacement of synchronous generators by converter-interfaced renewable energy sources requires wind farms to provide inertia, damping, and voltage support, particularly in increasingly weak grids. Based on classical frequency-domain loop-shaping techniques, this paper presents a coordinated multi-loop control design methodology of virtual synchronous machine (VSM)-controlled doubly-fed induction generators (DFIGs) in a wind farm to tackle the intra-machine controller interactions. Starting from an initial tuning and a full small-signal linearisation, every local open loop is redesigned to meet explicit phase margin targets through a single and prioritised iteration. The resulting controllers achieve step responses and stability margins close to those programmed at the design stage, despite the cross-coupling between control loops. Results can be improved further if a few more design iterations are carried out. Since the controller synthesis relies exclusively on classical loop-shaping tools available in commercial simulation software, it is directly applicable to industrial-scale projects.