My 8-year-old daughter has almost no interest in making friends. Her behaviors are not anti-social, but she seems perfectly content to play by herself, even when other children are present.
She will play with other children if she has no choice, and they usually seem to like her, but given a choice, she prefers to do her own thing.
My first suggestion is that you stop worrying.
In the first place, you've failed to convince me that your daughter's preference for solitary activity has to do with low self-esteem.
Research has established that whether a child is extroverted or introverted is strongly influenced by genetic factors. That means you can dismiss any worries that your daughter's social style is a parenting matter. You haven't caused her to be an introvert, and nothing you can do will turn her into an extrovert in 30 days or less.
Don't misunderstand me, however. The possibility your daughter inherited her tendency toward introversion doesn't mean this aspect of her personality is written in stone. This is not akin to inheriting blue eyes. Genes influence personality; they are not final determinants.
You've also failed to convince me that your daughter qualifies as shy.
A shy person feels painfully uncomfortable in most social situations and strives to avoid them. On the other hand, a "loner" by choice doesn't necessarily feel self-conscious or anxious when in social circumstances.
More often than not, the loner simply wants to be alone.
Most introverted children become more extroverted over time. The mechanism behind this transformation remains a mystery, but two factors seem important: first, parents who are themselves socially outgoing; second, parents who patiently encourage social interaction, as opposed to attempting to force it.
Along those lines, my second suggestion is that you stop trying to force something that can't be forced.
Trying to stimulate extroversion by matching your daughter with outgoing children isn't likely to work and may even make matters worse.
Introverted children tend to get along best with other introverted children. Pairing your daughter with an extroverted child may cause her to feel socially inadequate, in which case what is not a self-esteem issue could become one.
A disproportionate number of children who fit your daughter's description are highly imaginative and creative. If this is the case, I'd suggest that you focus on helping her develop her talents rather than obsessing about what you consider to be a deficiency in her personality.
To borrow from a familiar song, accentuate the positive!
The best thing you can do is simply stand back and let her find her own social comfort level and make her own social choices, even if they aren't exactly social.
John Rosemond is a family psychologist.