Refined coconut oil has close to zero coconut taste, depending on the brand.
A lot of the fear of cooking with olive oil is overblown. As long as you're not cooking over 375 degrees for long periods of time, and you keep your oil stored properly so it doesn't oxidize, it's good for cooking.
Beef tallow or lard work great. Try to find grass-fed fat (I get organic pastured pig fat at the farmers market for $1.29/lb) and render it down yourself.