As pointed out in the comments, SecureStrings have nothing to do with the Rijndael specification, and MCRYPT_RIJNDAEL_256 is not the same as AES256 (which refer Rijndael-128 with a 256-bit key)
So, to solve your problem, we just need a function to encrypt a plaintext in ECB cipher mode using Rijndael with a block size of 256.
For this, the obvious choice is the RijndaelManaged class. Fortunately, the MSDN documentation provides a basic but fully functional example of how to use the RijndaelManaged class and a CryptoStream to encrypt and decrypt strings - all we need to do is rewrite it in PowerShell and change the block size and cipher mode:
function Encrypt-Rijndael256ECB {
    param(
        [byte[]]$Key,
        [string]$Plaintext
    )
    $RijndaelProvider = New-Object -TypeName System.Security.Cryptography.RijndaelManaged
    # Set block size to 256 to imitate MCRYPT_RIJNDAEL_256
    $RijndaelProvider.BlockSize = 256
    # Make sure we use ECB mode, or the generated IV will fuck up the first block upon decryption
    $RijndaelProvider.Mode      = [System.Security.Cryptography.CipherMode]::ECB
    $RijndaelProvider.Key       = $key
    # This object will take care of the actual cryptographic transformation
    $Encryptor = $RijndaelProvider.CreateEncryptor()
    # Set up a memorystream that we can write encrypted data back to
    $EncMemoryStream = New-Object System.IO.MemoryStream
    $EncCryptoStream = New-Object System.Security.Cryptography.CryptoStream -ArgumentList $EncMemoryStream,$Encryptor,"Write"
    $EncStreamWriter = New-Object System.IO.StreamWriter -ArgumentList $EncCryptoStream
    # When we write data back to the CryptoStream, it'll get encrypted and written back to the MemoryStream
    $EncStreamWriter.Write($Plaintext)
    # Close the writer
    $EncStreamWriter.Close()
    # Close the CryptoStream (pads and flushes any data still left in the buffer)
    $EncCryptoStream.Close()
    $EncMemoryStream.Close()
    # Read the encrypted message from the memory stream
    $Cipher     = $EncMemoryStream.ToArray() -as [byte[]]
    $CipherText = [convert]::ToBase64String($Cipher)
    # return base64 encoded encrypted string
    return $CipherText
}
The decryption process is almost the same, although this time we'll need to reverse it and read the cipher text back through the CryptoStream from the MemoryStream:
function Decrypt-Rijndael256ECB {
    param(
        [byte[]]$Key,
        [string]$CipherText
    )
    $RijndaelProvider = New-Object -TypeName System.Security.Cryptography.RijndaelManaged
    $RijndaelProvider.BlockSize = 256
    $RijndaelProvider.Mode      = [System.Security.Cryptography.CipherMode]::ECB
    $RijndaelProvider.Key       = $key
    $Decryptor = $RijndaelProvider.CreateDecryptor()
    # Reverse process: Base64Decode first, then populate memory stream with ciphertext and lastly read decrypted data through cryptostream
    $Cipher = [convert]::FromBase64String($CipherText) -as [byte[]]
    $DecMemoryStream = New-Object System.IO.MemoryStream -ArgumentList @(,$Cipher)
    $DecCryptoStream = New-Object System.Security.Cryptography.CryptoStream -ArgumentList $DecMemoryStream,$Decryptor,$([System.Security.Cryptography.CryptoStreamMode]::Read)
    $DecStreamWriter = New-Object System.IO.StreamReader -ArgumentList $DecCryptoStream
    $NewPlainText = $DecStreamWriter.ReadToEnd()
    $DecStreamWriter.Close()
    $DecCryptoStream.Close()
    $DecMemoryStream.Close()
    return $NewPlainText
}
