Remember that when you are thinking in terms of the null hypothesis, the null hypothesis is that there is no effects (A=B). The null is the same regardless of what you think will happen. So if you think that the null hypothesis is true then a p value which is larger than the critical value would still lead you to fail to reject the null, the only difference is that a statistic which causes you to fail to reject the null is in support of your hypothesis.
Attempting to show support for a null hypothesis is difficult because, as you said, your statistical tests just aren't built to show that there is no difference. The way I usually see this problem handled (in psychology papers) is by acknowledging that it is not possible to prove a null result but to then emphasize why in your case it seems to be the best explanation of the current findings. To do this you want to show that the reason for the null finding is:
1.) based on good theory- you can explain both your findings and the findings of others in a way that makes sense in the context of the current literature,
2.)based on good statistics- your study has very high power so that the null result is not just for lack of the correct number of participants, and
3.) that your test came up far from significant- just use the standard test and show that p is above .05 (hopefully quite a bit above).