2.6 GHz microstrip patch antenna with 100 MHz bandwidth
According to your requirement you want a 3.8% relative bandwidth.
There are several techniques that you can use to achieve something like 10% of relative bandwidth if you are willing to slightly modify you design (number or layers or type of feeding)

Aperture Coupled feeding technique
Stacked multiresonator microstrip antenna
cavity loaded microstrip antennas

The first two approaches increase the bandwidth by exploiting the coupling between the microstrip antenna and the aperture feeding the antenna(case 1) or another passive patch antenna on top of the active one (case 2).
Approach 3) is based on the excitation of additional modes by loading the cavity with vias.
In my opinion i think you can reach 10% by combination of the first two approach
You can find more information about this approach in Kumar, G. and Ray, K.P. Broadband Microstrip Antennas