Methods for copying Time Machine backups offsite
If I understand your question correctly (and I may not) you would prefer a cloud solution but would be willing to consider another non-cloud offsite solution.

My preference is not to use the cloud for this type of backup. The cloud is fine for low volume data storage and file services (e.g. Dropbox, iCloud, Google Drive, MS OneDrive, etc), but for this type of backup it's not (at least not yet).

Instead, my recommendation is to do something similar to what I am doing. By way of example, I'll explain how I do this for my iMac (but I follow a similar process for all my machines!)


This iMac has a 500GB HDD
I have purchased two portable USB 2TB external hard drives
I have labelled these hard drives as iMac TM Backup HD 1 and iMac TM Backup HD 2
I set both of these external drives to be TM backup drives
As both drives are set up with TM they are alternated whenever both drives are available
Once the initial backups are done, I physically remove one of the external drives and take it 'offsite'
On the same day each week, I then swap them over
The net result is that both hard drives will have backups in the order of one week on, one week off (but between them I have a full set of backups).


Now, in terms of keeping one of them offsite, you have a number of options. Over the years I have used as my offsite location any of the following:


My workplace
A shed in the back yard
My car (but this may depend on your climate and where you 'garage' your car)
A family member's/friend's place (assuming you trust them!)


Basically, the idea is that your offsite drive is somewhere that protects your data in the event your house burns down or you get robbed. My strong suggestion would be in a locked drawer at your workplace (unless you work at home). Most people's workplaces are air-conditioned, secure, and convenient.

IMPORTANT NOTES ABOUT STORAGE

Regardless of the 'offsite' location you choose to keep your hard drive, there are some key factors to keep in mind:


Always keep the drive safe from large magnetic fields!
Ensure the location has a temperature range between 10 degrees celsius (50 degrees fahrenheit) and 43 degrees celsius (110 degrees fahrenheit). So, keeping it in a car would usually not be a good idea.