In which denomination(s) are Christians allowed to bury and hold a Christian funeral for their deceased nonreligious or just non-Christian relative? In which denomination(s) are Christians allowed to bury or hold a Christian funeral for their deceased nonreligious or just non-Christian relative in a Christian cemetery near the church? 

I am thinking about an instance where a non-Christian or nonreligious family member dies, and relatives just happen to be Christians. Do Christians ask their minister to perform a funeral for the deceased individual, or do they ask a humanist funeral officiant to do the job? Also, is there a general rule for allowing or disallowing non-Christians to be buried in a Christian cemetery, or is that more of a denominational sort of thing or is that up to the pastor to decide?
I haven't had to organize any funerals in this fashion, so this is going to be more of an opinion than anything.

I think that you should be able to perform a Christian Funeral for anyone, whether they be Christian or otherwise. 

@Mawia, I don't think that a Christian Minister would have a hard time preparing a message.

I grew up LDS (Church of Jesus Christ of Latter Day Saints {Mormon}) and when my Brother Passed away, my father asked me to speak.  So I picked something that I thought was relevant, I talked about when Jesus was on the Cross, his conversation with the two thieves, and the one acknowledged who Jesus was pretty much with his last breath, and Jesus said that he would be standing next to him in Heaven.  by doing this Jesus Said I don't care when you decide to believe in Me, I just want you to Believe in me.  pretty much saying you don't necessarily have to be baptized, that he knew this man's life was lived in Sin, but that the man saw the error of his ways and accepted that Jesus would save him, and that was enough for God's Grace.  

I think this message given at a Funeral might seem like a low blow, but when someone is at a funeral they need that hope that there is life after death, and need to know that God Cares, and that He is patiently waiting for you to Accept His Son, and give you Salvation.

I no longer claim to be LDS and at the time I didn't claim to be LDS either.  I claim to have a relationship with Jesus, and any church that helps that relationship grow is a good one.  

I think that most churches that claim to be Christian would have no problem performing a funeral service for someone that was not Christian.  The real question comes down to what the family wants.