What's the deepest coin you've found there so far? The park may have been heavily detected since the '70s. Also cities with a few parks have high budgets & may renovate with bulldozers & fill dirt. But because you've found war nickels (any wheat cents?), maybe those detectorists there before used high discrimination to pick out the silver.
I'm not saying to give up just because it's probably been detected many times, they may have missed some.
Fill dirt test: do trees that have long roots going way out from trunk show those roots? If so, maybe no fill dirt, at least around trees. If you see a type of tree known for roots that go way out, yet don't see those roots, fill dirt likely & coins will be deeper.
A 1934 park could have coins going back to 1880s, as 50+ years in circulation was common before coin collecting hobby grew.
When you can afford it, you might want to consider a higher-priced detector like the AT Pro to add another 2"-3" to your depth. But if you find a place not detected much & not renovated, you could find older coins within range of Ace 250 with DD coil. Best wishes, George (MN)