Cooney started his career at Athlone Town and Longford in Ireland before having trials with Celtic and being scouted by Manchester City.
He had been playing with Brentford’s development squad, but Cooney recently moved north to Leeds from London and has been on the look-out for a new club.
Joint-manager Paul Foot said: “Joe Lamplough broke his nose last week, Kieran McCaffrey was knocked out and Matty Plummer has joined Hull United, so we have been looking for somebody to come in.
“We pride ourselves in clean-sheets and because of that it is vital that nobody gets comfortable in their position.
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“Tommy can play anywhere across the back-four so that will add that competition and help us out.”
Foot is also impressed by the aims of progression that Cooney has.
He added: “Tommy wants to get back into the Football League, so he got in touch with us because he believes that we can help him with that.
“We have a proven record of relaunching players’ careers, all you have to do is look at Ben Middleton, Cameron Murray and others.
“Bryan Hughes has stacks of experience and contacts and I have picked up a lot from my days in non-league football, because of that people are showing an interest in what we are doing at Scarborough Athletic.”