TIFF has less contrast than PNG export

If you're actually facing the same problem, then stop working for a PNG in CMYK. There is no such thing as a CMYK PNG.   

Hi, to help - we need to know your colour spaces,

What's the ICC profile of the original CMYK working space??

I wonder if your PNG is RGB - perhaps without an embedded profile? That would mess this comparison up 

IS it for an injket print?
Are you working in the CMYK colourspace of the output device? generally it's considered better to work in RGB to get best gamut, even when printing to an inkjet machine with a RIP driving it]

When you save the file are you checking 'embed profile' [I recommend you SAVE or SAVE AS (to save a version) not EXPORT]

How are you viewing the saved tiff? does it have an embedded profile?

I hope this helps
neil barstow, colourmanagement net :: adobe forum volunteer:: co-author: 'getting colour right'
google me "neil barstow colourmanagement" for lots of free articles on colour management

How about reading the replies and providing the requested information? 

Please provide meaningful information about your problem including the requested screenshots of the layered image and the png (with Status Bar set to Document Profile). 

I am a little confused. Once you export as a .png it automatically converts to RGB so even though you are working in CMYK the comparision isn't accurate. You really need to compare the .psd to the .tiff and check the export settings. Perhaps posting your images here will help us see the problem.

Hi, to help - we need to know your colour spaces,

What's the ICC profile of the original CMYK working space??

I wonder if your PNG is RGB - perhaps without an embedded profile? That would mess this comparison up 

IS it for an injket print?
Are you working in the CMYK colourspace of the output device? generally its considered better to work in RGB to get best gamut, even when printing to an inkjet machine with a RIP driving it]

When you save the file are you checking 'embed profile' [I recommend you SAVE or SAVE AS (to save a version) not EXPORT]

How are you viewing the saved tiff? does it have an embedded profile?

I hope this helps
neil barstow, colourmanagement net :: adobe forum volunteer:: co-author: 'getting colour right'
google me "neil barstow colourmanagement" for lots of free articles on colour management

Where exactly are you choosing tif for export, is this in the camera or in photoshop? Might be the color profile you have set for tif does not have as wide a gamut. Can we please see the settings you are using for tif. If you are shooting this in your camera use the raw file format for best quality.

What happens if you convert the RGB png to RGB tif in photoshop? Should look similar. No such thing as CMYK PNG and don't ever use CMYK JPG is a msitake that they even allow that.

Please set the Status Bar to »Document Profile« and post meaningful screenshots of all three images (psd, tif, png). 

Can there even be CMYK-pngs? 

Edit: Ah, @Test Screen Name already posted! 

How are you comparing the contrast? What app and system?

If you reopen both TIFF and PNG in Photoshop, do you see the same contrast, or has it gone bad?

And by the way there is no such thing as a CMYK PNG ! If you export it will be converted to RGB.