We really do not have a specific scripture about demonic healings. Yet we do know that “…Satan disguises himself as an angel of light. Therefore it is not surprising if his servants also disguise themselves as servants of righteousness, whose end will be according to their deeds.” 2 Corinthians 11:14-15 (NASB20) Acting as an angel of light could include healings.
In another instance, a man named Simon saw that the apostles could bestow gifts of the spirit upon believers. Acts 8:17-20 (NASB20), 17 “Then they (?Peter and John?) began laying their hands on them, and they were receiving the Holy Spirit (?specifically the miraculous gifts?). 18 Now when Simon saw that the Spirit was given through the laying on of the apostles’ hands, he offered them money, 19 saying, ‘Give this authority to me as well, so that everyone on whom I lay my hands may receive the Holy Spirit.’ 20 But Peter said to him, ‘May your silver perish with you, because you thought you could acquire the gift of God with money!’” Obviously, Simon wanted to give gifts of the Holy Spirit which included the ability to heal others.
The begetting of the Holy Spirit in the early Church was indicated by certain miraculous gifts, but this was for a special purpose in connection with the establishment of the Church. As Paul pointed out, those gifts were intended to pass away. (1 Corinthians 13:8.) They were given by the “laying on of the hands of the Apostles.” (Acts 8:18.) Hence after the death of the Apostles these gifts were not bestowed upon any. And when those who had received the gifts died, the gifts themselves ceased – thus passed away.
A different approach to your question may be found in the Gospel of Mark. There Jesus was accused of casting out demons by the power of Satan. Jesus responded with a very interesting argument. Mark 3:23-26 (NKJV), 23 “So He (Jesus) called them to Himself and said to them in parables: ‘How can Satan cast out Satan? 24 If a kingdom is divided against itself, that kingdom cannot stand. 25 And if a house is divided against itself, that house cannot stand. 26 And if Satan has risen up against himself, and is divided, he cannot stand, but has an end.’”
We know that we are living in the end times and that Satan’s kingdom is coming to an end. Therefore, Satan’s house of demons is divided. The demons may indeed be working against each other. Jesus prophesied, “…there shall arise false Christs, and false prophets, and shall show great signs and wonders; so as to lead astray, if possible, even the elect.” Matthew 24:24 (ASV) Demonic healings may certainly be part of the deceptions. Let us watch and pray.