According to LDS teaching could Adam and Eve have children before the fall? 2 Nephi 2:23 states


  And they would have had no children; wherefore they would have
  remained in a state of innocence, having no joy, for they knew no
  misery; doing no good, for they knew no sin.


Often, it is said that Adam and Eve could not of had children, based on this verse. But the verse says would, not could.

Are there any other verses or latter day saint doctrine explaining whether or not they could have children?
In Doctrines of Salvation, 1:108, Joseph Fielding Smith stated:


  Things were not changing as we find them changing in this mortal existence, for mortality had not come.  Today we are living in a world of change because we are living under a very different condition from those which prevailed in the beginning and before the Fall of man.


Sometimes we focus too much on a single word, such as would vs. could.  I presume what you're asking is, was there anything physiologically stopping Adam and Eve from conceiving children?

Taking Pres. Smith at his word, the answer is "yes."  The time of the Garden of Eden was static.  Nothing grew, nothing died, nothing changed.  The moment you allow (e.g.) a child to be born you have something changing and that change must somehow stop when they become, what, 20 years old?  30 years old?  But, worse than that, you need to start dealing with the concept of (e.g.) dead skin flaking away from a growing child's body.  (Not to mention the changes to a woman's body when conception occurs, or the change of conception itself.)

Except nothing changed.

Therefore, no, Adam and Eve could not have physiologically conceived children in the Garden.  The physiological change that occured to them as a consequence of the Fall was necessary for conception.