The growing deployment of small Unmanned Aerial Systems (sUASs) in low-altitude airspaces has increased the need for reliable tactical deconfliction under safety-critical constraints. Tactical deconfliction involves short-horizon decision-making in dense, partially observable, and heterogeneous multi-agent environments, where both cooperative separation assurance and operational efficiency must be maintained. While Large Language Models (LLMs) exhibit strong reasoning capabilities, their direct application to air traffic control remains limited by insufficient domain grounding and unpredictable output inconsistency. This paper investigates LLMs as decision-makers in cooperative multi-agent tactical deconfliction using fine-tuning strategies that align model outputs to human operator heuristics. We propose a simulation-to-language data generation pipeline based on the BlueSky air traffic simulator that produces rule-consistent deconfliction datasets reflecting established safety practices. A pretrained Qwen-Math-7B model is fine-tuned using two parameter-efficient strategies: supervised fine-tuning with Low-Rank Adaptation (LoRA) and preference-based fine-tuning combining LoRA with Group-Relative Policy Optimization (GRPO). Experimental results on validation datasets and closed-loop simulations demonstrate that supervised LoRA fine-tuning substantially improves decision accuracy, consistency, and separation performance compared to the pretrained LLM, with significant reductions in near mid-air collisions. GRPO provides additional coordination benefits but exhibits reduced robustness when interacting with heterogeneous agent policies.