German term (edited): Maikaefer, Marienkaefer

I am an entomologist, and these are the terms I would use, although in the context of a nursery rhyme, the other terms such as ladybug may fit better, depending on the rhyming and the meter. Both of these insects, however, are beetles (order Coleoptera). May beetles, along with June beetles, cockchafers, Japanese beetles and dung beetles, and many others, belong to the family Scarabaeidae, from whence we get the word scarab, which of course is also in this family. Ladybird beetles are in the family Coccinellidae, and most species do indeed feed on aphids, scales, mealybugs and other harmful insects and are thus beneficial. I believe that Marienkaefer as well as the Spanish term Mariquita are both attributed to some medieval legend where, by a miracle, the blessed Virgin sent a large number of ladybird beetles to destroy a plague of aphids. Entomologically speaking, the term "bug" correctly applies only to the true bugs, order Hemiptera, which order includes such insects as the stink bugs, squash bugs, bed bugs and cinch bugs, and many others. In entomology, when an insect actually is a bug or a fly, its name is always written as two words (e.g., stink bug, house fly) and when it isn't a true bug or a true fly (order Diptera), it's written as one word (e.g., dragonfly, butterfly, mealybug). So if you're going to use the term ladybug, it should be written as one word because it's a beetle and not a bug. I've heard the term Junebug, but I can't say I've heard the term Maybug, but I suppose it does exist. Both May beetles and June beetles are members of the family Scarabaeidae and get their names from when they emerge as adults, often in great swarms. Scarab beetle larvae are the white grubs (Engerlinge) one finds in the soil. I remember vividly the swarms of "Junikaefer" the summer I spent in Innsbruck. All of this information can be found in any entomology textbook and countless websites.