Most likely you cannot, at least officially.
Mac mini late 2009 is only supported by macOS 10.13 (El Captan). But
Ollama requires 11.0 (Big Sur) or above.
LM studio only supports Apple Silicon macs.
If you really need to, you can compile
llama.cpp by yourself and do all the chores of model conversion, etc.
But the CPU is a bottleneck. The smallest model for DeepSeek r1 is 1.5B parameters. The
Intel Core2 Duo might be too slow for that. It doesn't even support SSE. Without vector instructions, the perf could be disastrous.