The best way for a blogger to respond to readers’ counter arguments is to

- Use evidence in a rebuttal.

Explanation:

The counterarguments are always supposed to be taken and responded positively and dealt using appropriate facts, logic, and evidence in order to establish the credibility of the claim as well as speaker or author himself/herself as negative response or ignorance may affect the image of the work.

As per the question, the most appropriate way for a blogger to respond to the counter-arguments of the readers would be 'using evidence in rebuttal' as it would substantiate the rebuttal and help nullify the counterclaim logically that promotes the enhancement of the reliability of the claim more evidently. This would assist in improving the validity of the blog and establish blogger's positive character among the readers.