A private key is just a 256-bit random number. (Well, a number between 1 and hex value FFFF FFFF FFFF FFFF FFFF FFFF FFFF FFFE BAAE DCE6 AF48 A03B BFD2 5E8C D036 4141.) All your computer does to make a new address is pick a new random number, and then do some math that calculates the public key from that number. There isn't any magic to it; it's just math. So, any way that randomly picks 256 bits will work. Computers tend to use fancy cryptographic libraries that find good sources of randomness from the information available to a computer, since they tend to be poor at flipping literal coins.

My comment was a probably-too-long offhand remark that you need some technology that you trust to keep your private key private. Sometimes simple technology is best, since you can see how it works and if it's sending your data elsewhere easily. But even if you were to literally flip coins, you'd want to make sure there wasn't a camera or somebody watching you that would compromise your random number generation. Really it's an analogy for what you need your key generating computer to be doing: picking good-quality random numbers that nobody else can end up knowing.