How do I add a System.Collections.ArrayList to a PowerShell custom object?

The challenge is to add a copy of the $fooChild [pscustomobject] instance you're re-using every time you add to the list with .Add() (if you don't use a copy, you'll end up with all list elements pointing to the same object).

However, you cannot clone an existing [pscustomobject] (a.k.a [psobject]) instance with New-Object PSObject -Property.

One option (PSv3+) is to define the reusable $fooChild as an ordered hashtable instead, and then use a [pscustomobject] cast, which implicitly creates a new object every time:

$fooCollection = [PSCustomObject] @{ fooChildrenList = New-Object Collections.ArrayList } 

# Create the reusable $fooChild as an *ordered hashtable* (PSv3+)
$fooChild = [ordered] @{ childName = ''; childAge = -1 }

# Create 1st child and add to list with [pscustomobject] cast
$fooChild.childName = 'Betsy'; $fooChild.childAge = 6
$null = $fooCollection.fooChildrenList.Add([pscustomobject] $fooChild)

# Create and add another child.
$fooChild.childName = 'Rolf'; $fooChild.childAge = 10
$null = $fooCollection.fooChildrenList.Add([pscustomobject] $fooChild)

# Output the children
$fooCollection.fooChildrenList

^{Note the $null = ..., which suppresses the typically unwanted output from the .Add() method call.}

The above yields:

childName childAge
--------- --------
Betsy            6
Rolf            10

A slightly more obscure alternative is to stick with $fooChild as a [pscustomobject] instance and call .psobject.Copy() on it to create a clone.

ArcSet's helpful answer provides a more modular solution that creates new custom-object instances on demand via a helper function.

Finally, in PSv5+ you could define a helper class:

$fooCollection = [PSCustomObject] @{ fooChildrenList = New-Object Collections.ArrayList } 

# Define helper class
class FooChild {
  [string] $childName
  [int]    $childAge
}

# Create 1st child and add to list with [pscustomobject] cast
$null = $fooCollection.fooChildrenList.Add([FooChild] @{ childName = 'Betsy'; childAge = 6 })

# Create and add another child.
$null = $fooCollection.fooChildrenList.Add([FooChild] @{ childName = 'Rolf'; childAge = 10 })

# Output the children
$fooCollection.fooChildrenList

Note how instances of [FooChild] can be created by simply casting a hashtable that has entries matching the class property names.

Quick copy paste from something I have that I use to make some of my Arrays. I have to create the custom objects and then add them to the Array. It will need modified for your scenario but I think it will get you what you need.

[System.Collections.ArrayList]$SQL_Query_Results = @()

ForEach ($SQL_Index in $SQL_Table) {

    $SQL_Array_Object = [PSCustomObject]@{
        'Computer_Name'    = $SQL_Table[$SQL_Index_Counter].ComputerID -replace ",", ""
        'Project'          = $SQL_Table[$SQL_Index_Counter].Project
        'Site'             = $SQL_Table[$SQL_Index_Counter].Site
        'Description'      = $SQL_Table[$SQL_Index_Counter].Description -replace ",", ""
        'Physical_Machine' = $SQL_Table[$SQL_Index_Counter].IsPhysicalMachine
        'Active'           = $SQL_Table[$SQL_Index_Counter].IsActive
    }

    $SQL_Query_Results.Add($SQL_Array_Object) | Out-Null
}

Edited to show how Array was initially created.