I ran into a similar situation recently, but I was trying to use a 11 meter antenna on 10 meters.
The antenna I had was a old Radio Shack antenna that was advertised as a "1/2 Wave Coaxial Antenna". Another name for this type of antenna are "vertical dipole". While the connection point is at the base, the actual feed point is in the center. But there was no way to trim the antenna for 10 meter use.
I initially thought of just building a 10 meter tuner, but thought there might be a simple way. So I read a bit about "Stub Matching". I had some short lengths of RG-8, with connectors, hanging around so I added a Coaxial-T at the feed point and started to add various length open stubs. I found that I could easily move the minimum SWR point down in frequency. In fact, I was able to move it to the 12 meter band. But I wanted to move the minimum SWR point up in frequency.
So I changed the configuration slightly and moved the Coaxial-T about 2' from the feed point. Then I attached various length open stubs from the Coaxial-T. Very quickly, the minimum SWR point was moved up to 28.150 MHz and gave be good coverage of the low end of the band, which is exactly what I wanted. The SWR is now about 1.2:1 at 28.120 MHz, where PSK31 is available.
If you have detailed information about your antenna feed point, it is a relatively simple matter to use a Smith Chart to calculate a stub. But I used a simple, unscientific, method or "cut and try". It does help to have a SWR bridge and a antenna analyzer. I used a older MFJ-259 to get the antenna in the ballpark and then the SWR bridge to double check it.
For dual band use, the stub could me made switchable.
