For sleeping among wild animals in Hilvarenbeek, April, May, June, July, August and September are usually the strongest months. During this period the weather is often more pleasant for being outside, a stay in and around the safari park feels more comfortable, and the experience is usually easier to plan.
Outside this window the atmosphere can still be lovely, but you will more often need to take fresher evenings, more changeable weather and less predictable conditions into account. That does not make the experience any less special, but it does make it a little less relaxed if you are mainly coming for a comfortable bucket list trip.
If you want to enjoy the experience mostly outdoors, spring or summer is the best time to plan it. If you are mainly looking for peace and quiet and care less about warmer temperatures, you can also look beyond the peak months.