How do monothelites explain Jesus' prayer in the garden of Gethsemane? ...monothelitism is the view that Jesus Christ has two natures but only one will. - Wikipedia


In the garden, Jesus prayed:


  Father, if you are willing, take this cup from me; yet not my will, but yours be done. - Luke 22:42 NIV


How do (trinitarian) monothelites explain this? Do they believe that the Son's will can vary from the Father's (in which case, why doesn't the Son's willingness to accede to the will of the Father also represent an expression of the Son's will); or that the first half of this prayer does not actually represent an expression of the Son's will (in which case, for what reason does he pray this - wouldn't it then be a disingenuous request)?
First, You may be conflating Trinitarian monotheism with monothelitism which does not meet the definition of Triniterianism. Trinitarian monotheism teaches that the Father, Son and Holy Spirit are not just one in will, but also one in substance.

Latter Day Saints, for example are monothelitic, but not monotheistic, teaching:


  Jesus Christ and the Holy Ghost are one in will and purpose but are not literally the same being or substance


And on this basis many Protestants believe that Latter Day Saints are not Christian or are unsaved - so this is actually pretty large distinction and not as pedantic as one might think.

In either event, the answer is the same for both the Trinitarian monotheist and the monothelitist. This is merely a dialectic conflict within the single will of God. 

This is the same dialectic conflict that any person might face who has a fear of, say, going to the dentist. You may be afraid and pray that your tooth pain would go away. You might plead and bargain to try to avoid the dentist, yet ultimately you go. You go because you know it is good for you in the long run. That despite your fear, you must go - that it is good for you in the long run. So despite your fear, you muster you courage, overcome your dread and fear, and you go to the dentist even though you don't really want to.

This does not indicate that you have two separate wills, but instead that you have mixed feelings and a fear of going to the dentist. You have an uncomfortable dissonance within your single psyche. The same is true of Jesus in the Garden. This does not signify two wills, but instead a fear of the coming thing that he has to do.