They advise you spend 2 hours minimum at the Beatles Story - it's actually split between two sites at the Albert Dock and Pier Head.
And you can't go all that way without going to the Cavern Club and Mathew Street, so allow another hour for that.
If you go on the Anfield Stadium tour you need to book a time slot, you can't just turn up. The stadium tour takes about an hour, but then you can go into the museum which you would need another 45 mins to an hour to see properly. And then of course there is the LFC shop.
According to the Everton FC website: "We hold Stadium Tours around Goodison on Monday, Wednesday, Friday and Sunday at 11am and 1pm. Tours do not operate on a match day or on the afternoon before a first team home fixture. Booking is strongly advised."
I would allow at least 2 hours for Goodison Park.
I think you would be able to do the Beatles Story (and the Cavern), Anfield and Goodison in a day, but you would need to plan it carefully and use taxis to save time.