As the Whites said, its the size of the charger, not the size of the generator that counts. The EU2000 itself can put out 8 amps at 12+ volts, but that isn't really intended as a charger. You will do beter charging via your trailers own converter/charger, which probably puts out at least 30A at full charge. You need to find out the converter/charger make and model to find out for sure - there should be a manual for it in the package of stuff that came with the trailer.
Two size 24 batteries (typical for your type of trailer) have a capacity of about 160-170 amp-hours and are probably 60-70% depleted if completely run down. That means you have to put back in .70 x 170 = 119 amp hours. If you could charge ata 30A rate, that would mean about 4 hours, but the charge rate will decrease substantially once the battery reaches about 75% of full charge. It takes many hours to get that last 20-25% into the batteries, so you would have to run for 8-10 hours to get close to 100%. It's more practical to stop at the 80% level and simply recharge more often. I's also better for the batteries to begin to recharge when they reach the 50% level, rather than drawing them further down.
If that's not enough power for you, I suggest adding a another battery, even if you just hook it in temporarily with jumper cables. More batteries will increase the amount of power available between the 50% and 80% charge levels and more batteries will charge faster than fewer will. Each battery can absorb some of the available charging current in parallel with the others, so you get typically better use of the available charging capacity.