Definitely do not parallel 2.2uF and 1uF ceramics, it makes no sense at all. Such mistakes easily happen when you "copy-paste" designs together, e.g. load-side IC datasheet specifying 1uF and regulator specifying 2.2uF. In this case, single 2.2uF would do the job, if the regulator is close to the IC. Or, if there is distance between them, use the same 2.2uF part at both sides.
One thing to be aware of is that some regulator ICs need certain amount of ESR to operate correctly, and therefore suggest usage of tantalum output capacitor; this recommendation should not be ignored. But if the regulator is MLCC-stable (i.e., stable down to some 10mOhm of ESR or so; and I recommend choosing such modern-day regulator), then just use enough output capacitance to meet the recommendation. They rarely tell you what is the actual capacitance needed, instead suggesting a nominal MLCC value. This can be problematic because capacitor A might lose just 40% of capacitance at the DC bias, while capacitor B loses whopping 90%. What did the manufacturer mean with their recommendation? The practical answer is to avoid the worst offenders, namely those MLCCs that just offer too much capacitance for the package size; so if 2.2uF is recommended, you don't need to use 4.7uF because you found out your chosen capacitor loses 50% of capacitance at the DC bias, because every other capacitor does it, too, and manufacturer took that into account. But if you choose a 2.2uF part which actually delivers only 0.22uF under DC bias, you are probably in trouble; maybe the regulator truly needs 1uF?
Usual internet advice of using the temperature tolerance 3-letter markings (like Y5V, X7R) to make conclusions related to other parameters than temperature tolerances, so to avoid certain stuff (like Y5V) and assuming that others (like X7R) have better DC bias characteristics, is wrong; X7R can colossally suck too. Similarly, the advice of picking higher rated voltage parts to then "derate" the voltage is similarly poor advice; a 10V and 25V part can be even the exact same part, both hitting 50% of rated capacitance at the same absolute voltage (e.g. 5V), not relative to their rating. Really, claimed volumetric energy density (claimed capacitance vs. package size) is the best indirect indicator of DC bias effect - in other words, if it seems too good to be true, it isn't. But nothing beats checking actual data if it's available.