They say it happened at around 20:00 on 28 December 2024.
The playground reopened before the new year, having been cleaned up by staff by 30 December.
In a statement, Guernsey Police said officers want information on five suspects, who were seen leaving the area by bicycle shortly after the damage is believed to have occurred.
“It is understood around five persons have thrown paint in the playground area causing it to be closed to the public for a short period of time while it was cleaned and then reopened,” said the spokesperson.
“Guernsey Police would like to hear from anyone that may have seen five individuals on bicycles, one of which wearing a high viz jacket making off from the area shortly after 8PM.
“If you have any information regarding this incident you are asked to contact PC 50 on 222 222 or to contact Crimestoppers anonymously on 0800 555 111 quoting OC2400009526.”