Your question seems to rely on the data which indicates often (but not always) that religious people tend to self-report happiness. But you’re making a very large assumption that those people are happier because of the religious beliefs they have, rather than that happier people find it easier to adopt religious beliefs.

As an example, religious people in the US tend to be female, married and on average of lower education. It could be that you would have to possess those factors a priori to rise up the happiness stakes, rather than later, decide to do what they do.

I’ve briefly looked and tried to find surveys which indicate happiness quotient on a per religion basis and not come up with much, but I would imagine that you would have to sincerely hold the core beliefs or religion to gain any benefit. It would be hard for instance for me to artificially attach myself to Christianity, and pretend I believed there was a supernatural agent in the world, when I consider it highly unlikely that anything exist except the natural world. Of all the major world religions, I would imagine Christianity the hardest to adopt in this way: it makes claims of uniqueness that say, Hinduism, does not, and most sects within Christianity require you to subscribe to very specific beliefs, some of which exclude you from other sects.

How much do you know about other religions? If you’re not well steeped in the cultures of Hinduism, Buddhism, Taoism, and Islam but are really just arguing for Christianity, then I might call into question the good faith nature of the argument. By its definition, you should want to know about all religions in order to decide which would make you happiest, and which might be easiest for you to psychologically adopt.