'wish' with past continuous tense

That is not the past continuous, it is the past perfect progressive.

The past perfect progressive tense describes a past, ongoing action that was completed before some other past action.

Before the budget cuts, the students had been participating in many extracurricular activities.

Before Jackie got home, it had been raining for three hours.

Therefore your sentences should be rewritten to use the past perfect tense.

I wish it had not rained so frequently (or so much) (when or while something else happened e.g. while I cycled from London to Bristol)

I wish it had rained more frequently (ditto)

I think this second person must be a farmer!