Coalescence time: Is it different for haploids and diploids in population genetics?

I'm trying to model Cyanobacteria cells divergence in 2 populations with mutation rate $-\mu$ and I need to verify my model with a valid theory. I don't have much biology background and all the theories I can find are either valid for haploid population or mating populations. All I need to know is a theory for coalescence time/divergence for a haploid population without mating. So far I have this:

$$T = 2\times N \times d\\ D = 2 \times \mu \times T$$ in which N is the number of diploid individuals, d is the number of subpopulations (in this case 2), T is the coalescence time and D is divergence. Can I apply this to my case even though it's defined for diploid population?

Thanks