If .us is best suitable suffix for a US located non-profit organization instead of .org, in a situation that .org and .com are not available? Or .net? or .agency?
or a domain name by adding "the" to it, like: theorganizationname.org
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If your organization is in another country, such as the United Kingdom, then .org.uk would be ideal.
If your organization has a specific purpose that falls into one of the newer generic top-level domains, then choosing a generic name might be better than .org. If you organization is a school, for example, then .academy could be excellent.
There are some little-used TLDs such as .help, .support, and .guide, too.
If you are a cooperative, then .coop is perfect.
The full list of TLDs may be useful to you.
You can always use a domain name that signals your nonprofit status: AwesomeCharity.us or non-profit.OrgName.com (and www.orgname.com would still work).