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Among the adjectives derived from nouns there some which do not bear Umlaut:

die Kugel - kugelig, der Monat - monatlich, usw.

But sometimes they do bear Umlaut:

das Jahr - jährlich, die Woche - wöchentlich, die Minute - minütlich, usw.

Some time ago I expected that monthly could be mönatlich but I was wrong. Is there a rule that helps by knowing when does the adjective bear Umlaut?

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There may be explanations for each and every case, I think the origin of the words plays a role, the first vowel shift and language change, e.g. which variant (lower vs high German) eventually found its way into our high German standard. But to a learner EM1's answer will most likely be the ultimate one. – bouscher Jul 26 '13 at 20:55
@bouscher -wöchig is also valid. – Em1 Jul 26 '13 at 20:55
@Em1 Ja schon, aber nur als Suffix, alle anderen Beispiele sind Vollworte. Der Viertelgeviertstrich dient ja hier nur als Worttrenner und nicht als Bindestrich. – bouscher Jul 26 '13 at 20:57
@Em1 genau, ich habe eigentlich das Adjektiv als Suffix gedacht: 2-wöchiger Kurs, usw. Aber es ist besser mit wöchentlich. – c.p. Jul 26 '13 at 21:01
Die Suffixe haben unterschiedliche Bedeutung: Ein zweiwöchiger Kurs dauert zwei Wochen, ein zweiwöchentlicher Kurs findet nur jede zweite Woche statt. – chirlu Jul 26 '13 at 23:21
up vote 2 down vote accepted

I think a look at will help you. You not only find a lot of examples and 'rules' for noun to adjective but also for all other possibilities.

In German: Nomen zu Adjektiv: Suffigierung
In English: Noun to adjective: Suffixation

Well, only issue is that you'll learn that the suffix -ig can lead to an umlaut but not necessarily.
Furthermore, you'll see that there are thousands of combinations. Have fun with burning them into your mind.

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