The problem is that the code you pass to reify is essentially going to be placed verbatim at the point where the macro is being expanded, and fieldMemberType isn't going to mean anything there.
In some cases you can use splice to sneak an expression that you have at macro-expansion time into the code you're reifying. For example, if we were trying to create an instance of this trait:
trait Foo { def i: Int }
And had this variable at macro-expansion time:
val myInt = 10
We could write the following:
reify { new Foo { def i = c.literal(myInt).splice } }
That's not going to work here, which means you're going to have to forget about nice little reify and write out the AST by hand. You'll find this happens a lot, unfortunately. My standard approach is to start a new REPL and type something like this:
import scala.reflect.runtime.universe._
trait TypeBuilder { type fieldType }
showRaw(reify(new TypeBuilder { type fieldType = String }))
This will spit out several lines of AST, which you can then cut and paste into your macro definition as a starting point. Then you fiddle with it, replacing things like this:
Ident(TypeBuilder)
With this:
Ident(newTypeName("TypeBuilder"))
And FINAL with Flag.FINAL, and so on. I wish the toString methods for the AST types corresponded more exactly to the code it takes to build them, but you'll pretty quickly get a sense of what you need to change. You'll end up with something like this:
c.Expr(
  Block(
    ClassDef(
      Modifiers(Flag.FINAL),
      anon,
      Nil,
      Template(
        Ident(newTypeName("TypeBuilder")) :: Nil,
        emptyValDef,
        List(
          constructor(c),
          TypeDef(
            Modifiers(),
            newTypeName("fieldType"),
            Nil,
            TypeTree(fieldMemberType)
          )
        )
      )
    ),
    Apply(Select(New(Ident(anon)), nme.CONSTRUCTOR), Nil)
  )
)
Where anon is a type name you've created in advance for your anonymous class, and constructor is a convenience method I use to make this kind of thing a little less hideous (you can find its definition at the end of this complete working example).
Now if we wrap this expression up in something like this, we can write the following:
scala> TypeMemberExample.builderWithType[String]
res0: TypeBuilder{type fieldType = String} = $1$$1@fb3f1f3
So it works. We've taken a c.universe.Type (which I get here from the WeakTypeTag of the type parameter on builderWithType, but it will work in exactly the same way with any old Type) and used it to define the type member of our TypeBuilder trait.