The crux of the argument is that in the 737-800 aircraft overhead bins fit rollerbags four wide, I'm sure these are at least 12" to 14" each, so you should be fine on a newer aircraft. Head to the back to find an empty bin for your use.
737-700 . 737-300/400/500. This is one of the later production 737-300 overhead panels. The air conditioning panel shows that it is not a 400 series and the digital cabin pressurisation controller shows that it is a late build aircraft. 737-300 . 737-200. Superficially very similar to the -3/4/500 panel. Differences include:
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boeing 737 800 overhead bin dimensions