And should your language be available, the classes would be much too easy for a bilingual child. Parents who want their children to go beyond spoken skills in the second language and who strive for literacy, usually end up teaching the kids themselves.
Homeschooling is a more common and more successful education option than one would think, especially in those countries where good schools can be expensive, e.g. USA. In some countries full time homeschooling is illegal, but teaching only one subject is fine, and just treated like any extracurricular hobby for a child. With so many people homeschooling in different corners of the world, there are plenty of materials, teaching instructions, and lesson plans available to get you started. The most ubiquitous resources happen to be in English and obviously focused upon teaching some other language. Even so, they can still be helpful for generating ideas. Here are many useful resources. You can always supplement with teaching materials for adults in order to find your own language mix, whether teaching Chinese in Finnish or any other combination.
When the alphabet of the majority language is the same as that of the second language, parents tend to wait until the child has learned the letters at school before beginning to teach it at home. Other children may show an interest in letters early and arrive at school knowing the minority language alphabet already. That is perfectly fine, although it is good to be extra clear with the teacher about it as Bryan from Auckland, New Zealand, learned.
"The teacher of my oldest son asked why Nathan knew all the letters, but had such a strange pronunciation of them. She didn't know my son was bilingual -- even though we had actually put it on our application. Anyhow, I think it took him less than a month to learn the English sounds for each letter (actual name of the letter and its phonic pronunciation)."
Teaching your child to read and write in the second language is a success most of the time, but some children (or their parents) find it 'too close to home'. Amy in Helsinki, Finland, is one parent grappling with this.
"I have found it to be quite a challenge for a Chinese non-teacher mother to teach written Chinese to my child. How do other parents manage this struggle? Do the children usually resist learning this from a parent, during the entire childhood?"
The best solution when there is mutiny in your 'home classroom' is usually to get a tutor. Ideally, gather some other families and have 3-5 school age children in a group. This will be more affordable, and the children will help each other. They don't need to be the same age, as long as their reading and writing proficiency are not too far apart. The other benefit to a tutoring group is that your child regularly meets other children who speak the minority language. That, in and of itself, is tremendously valuable.
Rest assured that home schooling a second language to your child is both common and successful. There is plenty of material, help and resources available on the web. Just let your fingers do the walking and you'll be off to a flying start.