Due to a limited budget, I wasn't able to conduct my experiment in one batch. Instead, I ran the experiment 8 times, twice for each genotype, with each batch containing both a control and treatment condition.

I attempted to add "date" as a variable in the DESEQ formula but ultimately got errors that kept me from including it in the end. I believe the error stemmed from a lack of replication within each batch.

Is it possible to account for a batch effect using this design?

You can estimate the treatment effect but you can't estimate the genotype effect, as it is confounded with batch as you've run the experiment.