High-quality, large-scale conversational datasets are scarce, making it difficult to train on-device language models (~1B parameters) as effective assistants. We introduce CoSy (Conversational Synthesis), a novel framework for generating diverse, steerable, multi-turn conversations at scale. CoSY combines three key mechanisms: (1) conversational graphs that ensure natural dialogue flow, (2) turn-based prompt augmentations for diversity, and (3) explicit linguistic phenomena for coherence. We evaluate CoSy on conversational grounded reasoning tasks (i.e. answering questions based on contextual information), a core on-device use case.Our on-device sized models trained on CoSy-synthesized data achieve competitive performance with human-annotated baselines and outperform instruction-tuned models of up to 70B parameters in zero-shot settings.