In one case the man approached a girl of 13 and asked for her phone number and tried to give her Â£10 before kissing her and running away.
Four incidents have taken place over the past six weeks, all in the Stoke and Earlsdon areas of the city.
Police described the man as aged about 20 and Asian or Eastern European.
The first reported assault took place at 11:30 BST on 9 September at a bus stop on Earlsdon Avenue South, where a 24-year-old woman escaped by getting on a bus.
In the other cases the victims, aged 17 and 18, were offered money for kisses and were assaulted when they refused, West Midlands Police said.
A man who has been roaming round Coventry sexually assaulting women and children after offering them money is being sought by police.