In view of Mark 9:1 why say the kingdom of God will come at Jesus' second coming? And he said to them, “Truly I tell you, some who are standing here will not taste death before they see that the kingdom of God has come with power.” (NIV)


Jesus was in the presence of his followers when he made the statement in Mark 9:1 that there would be some alive to see the kingdom of God come. When I listen to the radio or watch TV the message I hear quite often is that Jesus will come and establish a kingdom and reign for 1,000 years. If someone could explain this contradiction I would appreciate it.

I would prefer if when someone gives an answer that it be a biblical answer and not something based on a opinion. (people with a pre-millennium view)
To understand this verse you must have a clear understanding of what "The Kingdom of God" actually is.  A King's kingdom is where he is obeyed completely.  His rule and reign are complete.  So when Jesus uses this term it can easily be misinterpreted to mean a coming "thing" or heaven or some other such distant and more nebulous unexplained item.  

The more scripturally congruent interpretation is the one above.  Using those terms it is easy to see in Matthew 6:10  


  Your kingdom come, your will be done, on earth as it is in heaven.  


or in Matthew 6:33
But seek first the kingdom of God and his righteousness, and all these things will be added to you.   

Here in Matthew 7:21 


  Not everyone who says to me, ‘Lord, Lord,’ will enter the kingdom of
  heaven, but the one who does the will of my Father who is in heaven.  


shows that entering the kingdom of God is not possible without repentance, which is also congruent with Luke 13:3 and 13:5 


  No, I tell you; but unless you repent, you will all likewise perish.  


In Matthew 13:45-46 there is further congruence


  Again, the kingdom of heaven is like a merchant in search of fine
  pearls, who, on finding one pearl of great value, went and sold all
  that he had and bought it.


Clear after you apply the correct logical premise by comparing it to related passages in scripture.