I don't drink coffee, but my mom has a coffee maker into which she puts unground beans and which has a timer. So, basically, before she goes to bed, she puts beans in the machine, as well as water, and sets the timer. When she gets up in the morning, there's coffee waiting for her.

She seems to really like it.

Also, if paper filters are a problem, they make those reusable metal mesh ones that are rigid.

It's this one, or one quite like it.