How to calculate cutoff freqeuncy of Bandpass filter, given an attenuation dB level (OTHER THAN -3DB)
I assume you have an equation for amplitude vs. frequency? You just calculate the frequency at which it achieves the desired fraction of the peak value using algebra. Convert the dB threshold into a normal linear-scaled fraction using:

$$ y = 10^{\text{(threshold in dB)}/10} $$

For -3 dB, this gives 0.5012, approximately 50%.

For -1 dB, you would use 0.7943 and for -2 dB, 0.6310.

The expression might not look at nice when using decimals like these instead of the nice value of \$1/2\$, though.