The state has agreed Sharon Collins's conviction for conspiracy to murder her wealthy partner and his two sons by hiring an online hitman should be overturned.

The Court of Criminal Appeal heard the charge against the mother-of-two cannot be upheld as her co-accused was acquitted.

However Collins, who went by the name of Lying Eyes to find a hitman on the internet, is trying to overturn another conviction for soliciting a man to kill her partner, PJ Howard, and his two sons, Robert and Niall Howard.

She was jailed for six years on each count in November 2008 for plotting their murder. Her co-accused, Egyptian-born Las Vegas poker dealer Essam Eid, will also appeal against a six-year sentence for extortion and handling stolen property.

Tom O'Connell, senior counsel for the state, said as two people had to be guilty for a conspiracy charge, the state cannot uphold Collins's conviction. "Logically it is simply unsustainable," he added.

Collins, a petite 46-year-old, looked immaculate as she entered the courtroom in a smart black trouser suit and white shirt with her newly-highlighted blonde hair swept back. Her son Gary sat by her side until the case started.

Brendan Grehan, senior counsel for Collins, told the court the charges of soliciting referred to a date on or about August 15 2006 when it is alleged Collins and Eid agreed a hit contract and when she sent 15,000 euro to him by Fed Ex.

He said the appeal would focus on the trial judge's charge to the jury, the evidence of Teresa Engle, Eid's partner who was a convicted felon awaiting sentence in the US, the evidence of an alibi witness and the treatment of evidence relating to the poison Ricin.

Mr Grehan said the verdict for soliciting was tainted by the trial judge's failure to recharge the jury on the second charge. He called for the conviction to be overturned as he claimed neither the prosecution or trial judge dealt with the soliciting charge separately.

"They were not treated as separate offences and no attempt was made by the prosecution or trial judge to isolate the evidence," he added. The appeal continues.