Given you have the ID of the Journal Item (account.move.line) representing the AP debit from the Invoice and the ID of the Journal Item representing the AP credit from the Payment:

reconcile_wanted = self.env['account.reconcile.wizard'].with_context(
    active_model='account.move.line',
    active_ids=[__invoice_move_line_id__,__payment_move_line_id__],
).new({'allow_partials': True})
reconcile_wanted.reconcile()