I recommend finding an /r/ sound that your child can product successfully, and moving on from that. For example, if your child can produce the "er" sound, then try having her say the "ear" sound and the "air" sound since those vowels are all made in the front of the mouth. If you child can say the "are" sound, then try having her say the "or" sound since those vowels are all made in the back of the mouth.
If your child is having difficulty with all versions of vocalic R, then I recommend moving slowly from vowel to /r/. For example, the "ahhh" sound is easy to make since it is produced with the mouth wide open. Instruct your child to say "ahhh" like she does at the doctor's office; then pause; next, have her say the /r/ sound. Continue doing this, but decrease the pause with each practice. Finally, the pause will be eliminated and she can produce the "ahhh" and the /r/ as one, which is the vocalic /r/ sound "are." Practice the "are" sound several times thereafter. Here is how it will work:
ahhh..........r
ahhh........r
ahhh......r
ahhh....r
ahh..r
ahh.r
are
are
are.
This can be done with any vocalic /r/ sound.
If the problem your child is having is that the /r/ sounds more like a /w/ sound, then SLPs would call that "W-colored." One way to correct that is to remind your child that when she makes the /r/ sound, her lips should not be rounded. A great way to practice this is in front of a mirror. Have her look at your lips when you make an /r/ sound, then have her look at her lips; compare the two and highlight how her lips should be spread, not rounded. Another way to avoid this is to begin by avoiding practice on the "or" sound. The "or" sound requires that we round our lips, which can exacerbate the problem. Instead, start by practicing the other vocalic /r/ sounds and remind your child to keep her lips relaxed. Once you have mastered that, then you can move onto "or."
Please also keep these articulation tips from a previous post in mind when working on /r/: The /r/ sound can be difficult to teach and learn due in part because it is not a sound that can be seen easily on the face, such as the pressing of the lips with the /m/ and /b/ sounds, or the movement of the tongue with /t/ sound. One way to show your child how to make the /r/ sound is to remind her to raise and curl her tongue. Demonstrate to your child how a raised, curled tongue looks; then, have her practice this movement. Some children find it helpful to have the instructor gently push the tongue where it needs to be, either with a gloved finger or a tongue depressor. This cue is particularly helpful for children that produce an /r/ sound that mimics the /l/ sound. Another cue is what we call a "touch" cue. When making the /r/ sound, the sides of the tongue should touch the molars/wisdom teeth. Thus, remind her to feel this sensation. I found a link to a site where other SLPs shared their tips for eliciting the sound; here it is: http://www.playingwithwords365.com/2013/05/how-to-elicit-teach-the-r-sound/.
Here is a list of words that can be practiced at Rolling Hills Ranch:
"are"
start
far
tarp
farm
yard
dark
garbage
"er"
turn
learn
hurt
dirt
girl
together
trainer
stirrup
pasture
"air"
parents
where
square
mare
care
stare
fair
hair
carrot
"ire"
flier
tired
fire
campfire
hire
briar
admire
"ear"
fear
steer
hear
near
cheer
ear
pioneer
"or"
pour
sport
forest
for
thorn
morning
horse
horseback
more
north
horseshoe
To practice vocalic R at the phrase level, ask your child to describe some of the horses she sees. Targets may include "dark horse," "white horse," and "spotted horse." This works for other things with visual interest, such as "green pasture," "big forest" and "a lot of dirt."
To practice vocalic R at the sentence level, ask your child what she wants to do at the ranch. Targets may include, "I want to ride a horse," "I want to play with the girls," and "I want to meet the horse trainer." After you have toured the ranch or gotten on a horse, ask her to tell you what she did. (It's all right is this sounds a little obvious; you can explain to your child that you are asking her some questions to give her the opportunity to practice her speech.) Targets may include, "I rode through a forest," and "I saw animals on the farm."
To practice vocalic R in conversation, ask your child what her favorite part of visiting the ranch was. Targets may include, "I liked riding the horse. My horse was really nice. I thought I would be fearful, but I wasn't. I also liked the farm. But there was a lot of dirt everywhere!"