Although meant for data, the Zenodo repository assigns free DOIs. Nothing hinders one from uploading PDFs there.
Biorxiv (the main life sciences preprint server) gives DOIs.
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.
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.