Cockroaches and ladybugs are pretty similar. They both crawl sometimes and fly sometimes. They are both buggy looking and share much of the same DNA. But when a ladybug lands on someone they are generally really happy and make affectionate cooing noises. When a roach crawls up their leg they start screaming and try to whack the thing.
The first thing cockroaches should do is change their name. Ladybug and Christmas Beetle both sound nice, so I would go for something like Fortune Beetle or Wonderbug.
They also need to change their colours because brown just isn't working for them. I think glitterball would be pretty cool. Maybe they could have a big smiley face on their shells or perhaps they could just mirror the colours of the footy team in their local area. You would be far less likely to squish a Fortune Beetle who goes for the same team as you.