There are plenty of solar calculators and the brand of solar system you choose probably offers one.
Field day solar panel.
I see nothing in the rules about you must start field day with a discharged battery so i would plan starting with a fully charged battery having a fully charged battery in reserve and having a solar panel charging station off site to recharge the first depleted battery if you think your power usage would require more than one.
This is exactly what my club did.
Solar field day 2017.
That said there is a simple equation to calculate the amount of kilowatt hours kwh your solar panel system will produce.
5 hours x 290 watts an example wattage of a premium solar panel 1 450 watts hours or roughly 1 5 kilowatt hours kwh.
So a fresh deep cycle marine battery with 100w solar panel about 5a charge if the sun is good will run a kx2 at 10w all day with ease.
Watch out for the current drawn by the laptop as some laptops can be rather thirsty for power.
Perhaps a more economical mobile phone could be used.
How much energy does a solar panel produce.
So a rather small solar panel operated over a period of days could put enough charge on a battery to allow it to be used for the field day bonus.
As a heads up i hear solar power chargers can be very rf noisy.
A 10 ah lifepo4 battery was charged in the days prior to the contest using a solar panel a 10 watt panel will take approximately 18 hours of full sunlight to fully.