Hello,
Having 30 MHz bandwidth from a patch and wishing 200 MHz may not be feasible without sacrificing radiation efficiency or increasing the height above the ground plane.
Try to get the book: Compact and Broadband Microstrip Antennas by Kin-lu Wong.
By using a second or even two additional resonating structures, you can increase the BW with about factor 3, but this will not bring you close to 200 MHz. All designs that use multiple resonances in the patch itself of other structures increase the design complexity significantly.
The parasitic patch (as suggested by userdce) does really help, but increases the total height, unless you use patches adjacent to the main radiating patch
The problem in the gain can be caused by heat losses in the dielectric. The losses can be derived from the radiation efficiency and/or directivity. When the directivity is (for example) +2 dBi, you have good match and the gain is (for example) -2 dBi, you only radiate 40% of the electrical input power.
When you increase the conductivity of the conductors, you may only see a very small increase in radiation efficiency. This shows that in such a case dielectric losses are dominant. To increase gain, you have to increase the height and/or use better substrate material.
Note that when you use better substrate material (without increasing the heigth, you will get less useful bandwidth.