'Colourize'.
In British English: Colourise. American: Colorize.
And we're very upset that spell checkers make us choose between only American and British options.
OED says that -ize is equally "correct" to -ise. Australian spelling guidance has dropped the U in "color", "honor" etc.
I keep the "e" in axe, I spell metric measures (and centre and theatre) with "-re"
I still differentiate between advise and advice, practise and practice, defense and defence.
And I'd spell "check" as "cheque" except no-one outside the US still uses those. /s
'Colourize'.
In British English: Colourise. American: Colorize.
And we're very upset that spell checkers make us choose between only American and British options.