Yes, but you would need to file a separate 1040 for the child in their name in order to report an unused capital loss carryover amount.
Note: in this case, the IRS will be automatically running the income on the tax return against the income on their wage and income transcript database; it may be better-safe-than-sorry to report all the child's unearned income, to prevent an automated underreporting notice, (and any back-and-forth with the tax agency).
If reporting all the custodial 1099's on a child's separate 1040, verify that no tax is being calculated on any of the income amounts into the Form, on 1040 Line 24.
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