Although meant for data, the Zenodo repository assigns free DOIs. Nothing hinders one from uploading PDFs there.
Zenodo is a repository that assigns DOIs for free. You can access it via your GitHub account or ORCID ID.
There is a community-curated list of preprint servers, and it takes note of which identifier is assigned to content - you can filter those by DOI.
No preprint server should be charging authors any fees for DOIs? I would also +1 for BioRxiv or the Open Science Foundation has 18 different subject-based preprint repositories that might fit yours.
Biorxiv (the main life sciences preprint server) gives DOIs.