Can post-doc researchers write a recommendation letter for someone applying for a PhD program?

Academic rank varies by country. But I would expect in most places a letter written by a postdoc would be considered. Selecting letter writers is often a compromise between getting a letter writer who is highly ranked and well known and getting a letter writer who is well informed. Typically one gets both when a postdoc assists a senior faculty member in writing a letter.

Since the question asks about "a" recommendation rather than "the" recommendation letter, I think a post-doc letter is likely to be very helpful (assuming it's positive of course). Committee members are likely to give more weight to the comments in such a letter under the assumption that a post-doc is likely to have had more close contact with the candidate and can give a better assessment of their abilities than a professor.

However, I think that if the only recommendation letter was from a post-doc, that would be less good, because they'd also like to see a faculty member's opinion. A professor may not have as much contact with the applicant and can't do as good a job evaluating personality and technical ability, but they can probably do a better job of comparing this particular applicant to many others in a similar position, while a post-doc can do a more detailed assessment but probably has fewer similar people to compare to.

Including letters from both would cover both bases and, I suspect, would be a stronger application than having two letters from professors.

If the postdoc has a very good understanding of you (ie: you worked together on a research project), it may actually be better than run-of-the-mill "She was an A-student in my class ..."-letters. I would ask the postdoc to really reflect on your skills; as someone that is still very active in research, the postdoc's opinion may be very worthy.