I'd just use 'or' and say the magazine was published on a weekly or monthly basis. 'irregular publication schedule' doesn't work as it implies there are periods in time when the magazine is not published at all - not the same as what you are trying to say. Even if you said the magazine is published irregularly weekly or monthly, it doesn't work - it's still implied there are weeks or months when it is not published.

There is no phrase for something that is published with different, random frequencies. The best words to use would be intermittent, irregular or sporadic. "The magazine was published intermittently" "The magazine was published irregularly" "The magazine was published sporadically"

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