Why is it you want peat free? If it is for better drainage, then adding coir negates the effect. The coconut coir is a substitute for peat that accomplishes the same things, which are loosening the soil up a bit, making it lighter and fluffier AND holding water. If you are avoiding peat because of its acidity, then coir is a good substitute being pretty close to neutral (pH 6 -6.8 ). Coir is also easier to re-wet once dry than peat, which is good in a cactus mix that you want to dry out between waterings.
To make a free draining cactus mix, you can use some compost, some coir, maybe some bark fines, but mixed with a whole bunch of something inorganic, pumice, perlite, chicken grit, sand, etc. I can't give you any exact recipes, because I don't grow cacti and succulents.