Given that the required advice tended to be along the lines of "How do I get out of this mess?", it is curious that the boot should now be on the other foot, with Royle eyeing up a place in Europe and Atkinson seeking a route to survival.
Even after losing only twice since Christmas, Atkinson's Coventry are precariously placed, but Royle has every confidence in his mentor's ability to defy the odds.
"I hope they stay up, for Ron's sake," he said. "And I think they can because they score goals, which was always Oldham's saving grace. It may sound an obvious thing to say, but if you can score goals, you can win games."
This simple truth remains the cornerstone of Atkinson's philosophy. Only last week he admitted he got bored coaching players to defend. "Quite frankly, I'm more interested in scoring goals than stopping them," he said. This may be Atkinson's last season as a touchline manager and he is not about to learn new tricks.
But the old ones might yet work; indeed, they almost did on Saturday, on Royle's patch.
Stunned by Everton's 25-minute two-goal opening, upset by the loss of Noel Whelan, who needed six stitches in a head wound after an accidental clash with David Unsworth's boot, Coventry could have been on the painful end of a walloping.
But their response was never less than positive, their approach never less than courageous, a quality clearly inherent in Whelan, whose last contribution was to win the corner from which Coventry pulled back their first point-saving goal.
Thereafter Everton, not helped by the withdrawal of Joe Parkinson to another first-half injury, lost their grip and Coventry, prompted off- field and then on by Gordon Strachan, took the initiative.
Two goals from Duncan Ferguson, bringing his tally to seven in 10 starts, had suggested that Everton, at last able to pick Marc Hottiger, would be weighing up their last eight matches from fifth place. Instead, they remain seventh, although still on course for Europe and a far cry from the anxious days of last October, when they slipped to 16th. Coventry today are just one place higher. Not that Royle would be so impertinent as to offer advice, nor Atkinson to want it.
Goal: Ferguson (17) 1-0; Ferguson (25) 2-0; Daish (38) 2-1; Williams (85) 2-2.
Everton (4-4-2): Southall; Hottiger, Unsworth, Short (O'Connor, 89), Hinchcliffe; Kanchelskis, Grant, Parkinson (Amokachi, h-t), Ebbrell; Stuart, Ferguson. Substitute not used: Limpar.
Coventry City (4-4-2): Ogrizovic; Borrows, Busst, Daish, Shaw; Telfer (Strachan, 69), Jess, Williams, Salako; Whelan (Ndlovu, 42), Dublin. Substitute not used: Filan (gk).
Referee: P Danson (Leicester).
Booked: Coventry: Daish, Borrows, Telfer.
Man of the match: Ferguson.
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