EDIT: As the OP points out in his answers, this should be:
(with-eval-after-load "paren" (add-to-list 'show-paren--context-child-frame-parameters '(background-color . "black")) (add-to-list 'show-paren--context-child-frame-parameters '(foreground-color . "red")))
Original answer
Try:
(with-eval-after-load "paren" (add-to-list 'show-paren--context-child-frame-parameters '((background-color . "black") (foreground-color . "red"))))
Stick the above in a file foo.el , start with emacs -l foo.el and test. If it works, adjust colors to taste and move the code to your init file.
Completely untested.
show-paren--context-child-frame-parameters: that's what's used when making the child frame. Untested - no guarantees.