Will there be sin during the Millennial Reign?

Based upon multiple sources, the answer is both yes and no, primarily being no. It appears that Satan is bound for 1000 years based upon the verse below:

“He seized the dragon, that ancient serpent, who is the devil, or Satan, and bound him for a thousand years” (New International Version, Rev. 20.2).

However, for those who do not receive glorified, resurrected bodies, sin and temptation will still be able to affect these people, if this is indeed what will take place.

Who are these people? 

Those who survive the tribulation and have children who have children and so on. These people will still have their normal, earthly bodies and it appears sin is passed down – similar to, if not, generational sin if this indeed takes place.

Some of these people will then do the following:

When the thousand years are over, Satan will be released from his prison and will go out to deceive the nations in the four corners of the earth—Gog and Magog—and to gather them for battle. In number they are like the sand on the seashore. They marched across the breadth of the earth and surrounded the camp of God’s people, the city he loves. But fire came down from heaven and devoured them. And the devil, who deceived them, was thrown into the lake of burning sulfur, where the beast and the false prophet had been thrown. They will be tormented day and night for ever and ever. (Rev. 20.7-10)

In summary, those who receive glorified, resurrected bodies will not be affected by sin, whereas and possibly speaking, those who survive the tribulation (which will presumably be a smaller number of people) and will likely have children, will still have sinful desires. However, those with glorified, resurrected bodies could possibly have children as well.