My wife and I are planning to visit Kunming in summer for two months.
I'll use that time to study and improve my Chinese, so I'd like to stay somewhere close to the city center / Green Lake Park.

Two months are too long to stay at a hotel but too short to sign a proper rental contract.
Airbnb charges ridiculous fees, although prices are still cheap due to the low baseline. Chinese short rental websites mostly require you to own a Chinese bank account and ID card and I have no idea which service is trustworthy.
Then there's also the issue that I'm a foreigner so that I'll need a landlord who is willing to come with me to register at the local police station.

Sharing the flat with others isn't really an option either as the wife's expectations regarding hygienic standards differ from the customs of most locals.

So I'm wondering, what is the best way to rent an apartment for 2 months in Kunming?

It may help you if you register properly with a local language school first. Find one who is willing to help you find suitable accommodation. Most will.

there are a fair few apartment style accomm options on the regular booking sites like agoda and booking.com etc. some very reasonably nightly rates, so staying a month or two these are an option.

I have brought my kids to Kunming for a couple months at a time, cos that's the longest we've been able to stay in the past too...and these apartments have been a good option.

We had a few offers of local apartments this time, but many are unfurnished and so not really appropriate to buy all the stuff if u r only staying a month or so.

At least apartment style accomm that is aimed at tourists will have all your basic cooking needs and bedding etc.

I am a foreigner and at my local PSB I have never needed my landlord to go with me to register, I just needed lease and photocopy of his ID the first time, when I moved in. Later trips in and out of the country, I just had to show up with my passport - did this last week.

If you do not have a lease because you are a short term rent, you may need some other form of documentation from the local PSB. Perhaps this is why the OP mentions the landlord.

Check the classifieds here when closer to summer. Sometimes you see ads here for short term letting.

I'd rather develop the ability to book and negotiate stuff myself, as I might not always go to a school when I visit Kunming / China in the future.
But I really like the idea to stay at an apartment hotel. However, those websites always limit booking time to like 30 days. Is there a website that offers longer reservations?

You could have just said you don't want to share without mentioning your hangups about hygiene. And Alien is quite right. Landlords don't go with you to the PSB. If they had to nobody would get registered.

So how is it supposed to work when you are renting a sublet flat? Is it now enough if I just print out the booking confirmation from the (usually english) Website, or what documents are needed?

I lived in a shared flat like five years ago and the PSB at Wenlin Street insisted that I take my landlord along who had to take his rental contract and ID card with him and sign a form provided by the PSB. Did this change since?

@Alien or so they don't ask for the rental contract at all anymore?

@kurtosis:

Alien wrote the FIRST TIME he registered at A NEW ADDRESS he needed his lease and a photocopy of the landlord's ID. ---THE FIRST TIME---.

Once you are registered, the registration is computerized, and the registration is good for the duration of your visa/residence permit (date in your passport).

If you leave China and return, or get a new visa/residence permit, or a new passport, you need to return to the same PSB office and have your record updated.

The ladies at the PSB office are experienced with clueless foreigners with no ability to speak Chinese and/or do not understand the process. Generally, they are helpful and solve problems.

I learned to bring a photocopies of:
1) the lease with the landlord's ID attached,

2) passport ID page,

3) reentry stamp in the passport page,

4) the new visa/residence permit page
5) passport photos

6) landlord's phone number

The ladies would find what they needed and would return what they did not need. I kept all the stuff in one envelope, adding new photocopies as needed, and brought everything each trip to the PSB.

The registration is YOUR responsibility and if the school, employer or friend screws it up, or is LATE, YOU suffer.

The process is easy, takes about 15 minutes, and forgiving IF YOU SHOW UP to do it. Chinese people do not need to do this and most know less than you do about the process, spouses excluded.

After being threatened with deportation and signing a confession because somebody screwed up, I always did it myself rather than rely on a Chinese to do it for me.

NOTE: There is a 20% tax on rents paid (or, it was 20%) which is why landlords are not cooperative and rents are higher for foreigners. The last person to trust to get this done is the landlord.