Judge David McHugh refused bail for Core and remanded him in custody to appear before Cloverhill court on Friday.
The judge remanded Smith on bail to appear before the court again in March.
Core, of Druid Court in Poppintree, and Smith, of Riverwood Crescent in Carpenterstown, appeared before Blanchardstown District Court charged with robbery.
The alleged incident took place at Molloy's Liquor Store, Clonsilla Road, Clonsilla, on January 18.
It is alleged that up to €1,080, was stolen during the course of the robbery.
In relation to Smith, Garda Conor Mallen said there was no objection to bail subject to an independent surety of €800.
Judge McHugh remanded him on bail to appear before the court again in March for DPP's directions on the matter.
Garda Mallen objected to bail for Core, citing the seriousness of the charge and the strength of the evidence.
The garda alleged that Core entered the off-licence armed with two imitation handguns. He threatened staff and forced them to hand over a sum of money.
Garda Mallen claimed that Core was caught on CCTV cameras, was identified by staff and that fingerprint evidence places him at the scene.
Defence solicitor Matthew Kenny said Core would abide by any bail conditions.
Judge McHugh refused bail and remanded him in custody to Friday.