Five of the seven arrested last week on suspicion of plotting to kill Vilks over his cartoons depicting the Muslim prophet Muhammad as a dog have now been released.
Ali Charaf Damache, 44 and from Algeria, appeared in court charged with sending a menacing text message, said Irish state broadcaster RTE.
Abdul Salam Monsour Khalil Al-Jahani was charged with an immigration offence at the court in Waterford, southeast Ireland. The 32-year-old Libyan is accused of failing to produce correct identity papers.
They were remanded in custody and will appear in court again on Friday, said RTE.
According to the Algerian man's counsel, Brian Chesser, the charges are a way for the police to continue to keep his client in custody, and he thinks that more serious charges will be levelled later.
The men were part of a seven-strong group arrested last Tuesday over an alleged plot to assassinate Swedish cartoonist Lars Vilks, who has a $100,000 bounty on his head from an al-Qaeda-linked group.
Another suspect, a Croatian man, was released without charge on Monday after six days of questioning, Irish police said.
Only two of the seven people arrested have now faced charges. The other five - three women and two men - have been released without charge in recent days.
Files are being prepared for the country's director of public prosecutions, according to police.
Those originally arrested were three Algerians, a Libyan, a Palestinian, a Croatian and a US national, a police source has told AFP. They ranged in age from mid 20s to late 40s.
The controversy started when Swedish regional daily Nerikes Allehanda published Vilks' satirical cartoon in 2007 to illustrate an editorial on the importance of freedom of expression.
The cartoon prompted protests by Muslims in the town of Örebro, west of Stockholm, where the newspaper is based, while Egypt, Iran and Pakistan made
An Al-Qaeda front organisation then offered $100,000 to anyone who murdered Vilks - with an extra $50,000 if his throat was slit - and $50,000 for the death of Nerikes Allehanda editor-in-chief Ulf Johansson.
The protests in Sweden echoed the uproar caused in Denmark by the publication in September 2005 of 12 drawings focused on Islam, including one showing the prophet Muhammad with a turban in the shape of a bomb.
Last week, the Irish Independent newspaper reported that a suspect known as "JihadJane", the online name of Colleen LaRose, had spent two weeks in Ireland last September on a "fact-finding trip" before her arrest in October.
LaRose has been indicted for recruiting jihadist fighters in the US, Europe and Asia in a bid to carry out terror plots.
She was reportedly monitored with a couple in Cork and Waterford in southern Ireland, where the seven were arrested.
US prosecutors said that LaRose had agreed to carry out the murder of a Swedish resident, pledging "only death will stop me."
The US Justice Department has declined to say if LaRose was connected to the alleged plot to kill Vilks. The Washington Post has cited government officials who confirm the link.