Since he won't be eligible for a Pokemon Trainer License until 2025, Raptor-Son and I are working on a good curriculum of games that he can play. At four months, your options are relatively limited, but I thought I would share some of the games he seems to like the most. I'm reasonably sure these are developmentally appropriate and safe to play. Raptor-Son hasn't complained yet.
1. The Bouncer
Raptor-Son has a complicated relationship with his bouncer seat. He'll sit in it for about ten minutes with a resigned look on his face, and then slowly start to break down until we rescue him. He begins with some standards grunts, moves on to a little yelling, and then starts crying with his lower lip out if no one has saved him from its polyester clutches. However, if you bounce and play with him in there, he's much happier. He loves it if you bounce him, and then as he's coming back up, you get your face in real close to his and smile in a giant way. He also likes it if you play with his feet and in general distract him from the fact that he's in his bouncer at all.
2. Making Faces
Classic. He's at the age where he has started to like people making faces at him, and although he hasn't started to imitate them yet, it's still fun to watch his goofy open-mouth smile. Any funny face is good, and he particularly likes if you shake your head and let your tongue roll around. Ideally, you also start about eight inches away, and then rapidly move your face in toward his. This is how we got him to giggle for his first time.
3. Tickling
Another classic. I don't think he's strictly speaking ticklish yet, but he nonetheless likes it when you tickle on his chest and arms. For maximum effect, combine with Faces and The Bouncer.
4. Peaches, Peaches, Peaches, Plums
So this is a thing I never thought was weird, but it turns out only my family does it. Raptor-Son is a huge fan of it, so please steal it if it works for you. Put the baby on his back, and hold one foot in each of your hands. The basic idea is to touch his feet together three times, each time bringing them closer to his nose. On each almost-touch, you say "Peaches," until the fourth one when you say "Plums!" and then bring his feet back down. I don't know why those fruits, and not "One, Two, Three, Four" or something, but there we are. He loves this one.
5. Tuck In
This one I discovered on my own when I needed to make the bed while keeping track of him. It requires some supervision, but he likes it a lot. Prop your pillows up at the top of the bed, and then place him sitting up in between them. Then I pull the sheet up, then the quilt. Then I go to the bottom of the bed, and take the bottom of the quilt, and bring it up and then down quickly to make a wave. The wave will blow air on him, and he giggles and laughs. This lets you entertain him, but also make the bed.
6. Baby Elevator
I debated including this one, because it's more of a fun thing for me and less for him. I just hold his torso, and lift him up over my head. It's a good workout for me if you do some repetitions, although it seems more like he tolerates it, rather than having fun. He always stops crying, and looks around. He also planks his legs out usually, so it's good Tummy Time exercise for him too.
Hopefully these will keep your own infant's fussing to a minimum!