Okay, I'm very, VERY new to the battledome. I bought my peophin a bunch of stuff like the jewelled peophin mask, the peophin saddle, shield, sword, hooves, blinkers, and medallion. It cost me around 40k, which isn't too bad. ever since I bettled him, and won, he's been unhappy. how come???? Is it the battledome or something else?
I don't think the battledome would do that to your pet. My pet is also constantly sad and I try everything I can too cheer it up but it doesn't work. Maybe its just neopets :S
About your set. I think you should ask for help in the help section of the site. Species weapons (example: weapons only for the peophin) arn't always the best deal. They are usually pretty weak. I can see you are new to the battledome and there is a lot to learn about icons, defence, reflection, freezing and so on. You've come to the right place.
I also see this is your first post. Welcome to the forums ^_^
Oh wow, hi! You finally posted. Welcome
Anyway, what ben said is correct. Battledome might not necessarily be the thing that makes him unhappy, though nothing a quick play can't help.
If you would like help on your set feel free to post at the weapon advice section. Plenty of people there who will be more than happy to give you advice, me included.

Musical instruments can help. I'm convinced that they increase happiness faster than toys. Also try those tours like on kiko lake. Hope it helps.
I don't like how looks the peophin but it has some nice features.
Peophin Splash (Level: 20) 2 Water & 2 Light. Then 1 more water and after that 1 more light. At max. 6 total icons of a mix that i like it -some don't-
Full Peophin Armour 3(air, fire, physical)+2earth
Golden Peophin Harp a freezer+2 dark of defense
Jewelled Peophin Face Mask Def 2(Light,Fire,Water,Physical)
Mighty Peophin Helmet 3(earth, light), at least 3 icons will past burrow and sink, and def. 3 dark.
But some of them (especially the freezer) would be expensive and hard to find, because rarity.
WELCOME! if you have any doubt just ask someone will answer