That's a typical problem with any shortened antenna,
especially on 80m. A poor ground will make it wider
at the expense of performance, but not enough to
cover the whole band.
Even a full-sized 80m dipole will have an SWR bandwidth
below about 250 kHz at the 3 : 1 points.
So one of the first questions is, how much bandwidth to
you want? If you just want to operate the DX window,
or CW at the bottom of the band, you may be able to
manage. An antenna tuner will extend that somewhat,
too.
One way I've extended the bandwidth on a trap vertical
that uses a mobile resonator at the top to cover 80m is
to remove the radiator and add a 40m trap plus longer
horizontal wire around 30' to resonate the antenna as
needed. In one case, I made a wire stub with part of
the top loading wire to serve as the trap inductor.
To cover more of the band, you can use a screwdriver
antenna with as long of an extension on top as you can
manage - that should allow you to remotely tune it
across the band, and possibly on several other bands
(depending on the top length).
There are wideband antennas that over the whole 80m
band, but they typically will be close to a full-sized
dipole or larger. Terminated folded dipoles can cover
the whole HF band with low SWR, but you can give up
4 - 10 dB of signal strength to do so.
Here is the
80m wide-band dipole that I've used a few times.
Here are some of
W4RNL's notes on wide-band 80m antennas.
Or you can put up
something like this...