If there is someone in town who is good at teaching preschool music, go for it.
See if there is someone licensed in Kindermusik.
That's a curriculum which makes music a fun and gregarious activity for preschoolers.
If that works, then you can invest in a violin if there is also a Suzuki teacher in the area.
The most important variables are patience and creativity on the part of the adult.
Here are some ideas which I have used with preschoolers:
■ manipulating wooden cut-out notes
I start with quarter notes and eighth-note couplets only.
That's plenty enough for a preschool beginner.
■ manipulating oversize notes
I start with so and mi.
In Lois Choksy's books, there is a compilation of songs using only these two notes.
That's plenty enough for a preschool beginner.
■ melodic dictation
Hum so mi so so and ask the child to play it.
With only so and mi, this activity can last longer than you might expect.
If you limit the activity to 4/4 measures using only quarter notes, that gives you 16 possible rhythms.
If you add in eighth note couplets, that brings it up to 256.
Preschoolers sometimes like to reciprocate.
If the child wants to dictate measures to you, I hope you don't mind.
■ measure search game
With the score for the song in front of you, play one measure from the song and ask the child to identify.
If the child wants to reverse roles, don't take it personally.
In fact, that's good, because the game lasts twice as long that way.
■ rhythmic dictation
"Show me quart quart eighth-eighth quart."
Again, if the child wants to turn the tables, I hope you will be a good sport.
■ transposing
Show the child where the two notes are for the two-note songs in all 12 keys.
This may bore the dickens out of an adult, but preschoolers love it.
■ card games
Make a card deck consisting of 2 cards for each of the 16 possible 4/4 rhythms using quarter notes and eighth-note couplets. If that's too much to handle, use only a few cards out of the deck.
At first, a preschooler might not understand any card game except the memory game, but after a while, he or she can understand old maid and go fish.
■ ostinatos
An ostinato can be very simple.
While you sing or play a bichordal song, such as Mary Had a Little Lamb or Skip to My Lou, the child can repeat the fifth note of the scale.
If the child enjoys it the first time, do it 11 more times in all the other keys.
There have been compositions written for exactly this purpose. Exploring the Piano by Alexander Tcherepnin is a good one.
Anything involving permutations is good.
I once worked with a 3-year-old using a set of bells and a chord organ.
While I played the bells and she played the chord organ, I chanted the child's name on all 12 major chords and all 12 minor chords.
Then she asked me to do the same thing on the words "Mommy" and "Daddy."
Then she asked me to trade instruments and we performed the whole ritual all over again.
If anyone ever tells you that "preschoolers have a 5-minute attention span," remind them that the number 5 can be multiplied.
If you have at least 12 different activities, the child can last for a whole hour.
I know because I've been there and done that.