The two injured men, aged 42 and 62, were targeted at a house in Bridgeburn Drive at around 9.15pm on Saturday, October 10.
Police are looking to find a man seen at the front door shortly before the attack - described as being in his mid-40s or early 50s, around 5ft5in tall, and wearing dark clothing.
Detective Sergeant David Lamont, from Lanarkshire CID, said: “This appears to have been a targeted attack where the person responsible has used extreme violence towards both males causing them to be hospitalised.
“I believe that the local community may have information that could help identify the person responsible and I would appeal to them to get in touch.
“Anyone with information is asked to contact Lanarkshire CID Coatbridge on 101.”