In an intriguing article, Stephen Kosslyn proposes as his most "dangerous" idea the proposal that God is both real and accessible to science:
Here's an idea that many academics may find unsettling and dangerous: God exists. And here's another idea that many religious people may find unsettling and dangerous: God is not supernatural, but rather part of the natural order.
Simply stating these ideas in the same breath invites them to scrape against each other, and sparks begin to fly. To avoid such conflict, Stephen Jay Gould famously argued that we should separate religion and science, treating them as distinct "magisteria." But science leads many of us to try to understand all that we encounter with a single, grand and glorious overarching framework. In this spirit, let me try to suggest one way in which the idea of a "supreme being" can fit into a scientific worldview. I offer the following not to advocate the ideas, but rather simply to illustrate one (certainly not the only) way that the concept of God can be approached scientifically.
1.0. First, here's the specific conception of God I want to explore: God is a "supreme being" that transcends space and time, permeates our world but also stands outside of it, and can intervene in our daily lives (partly in response to prayer).
To begin a science of the divine, we will need a workable concept of what a God/Goddess is, and to clear away some theological misunderstandings that have pitted science and religion against each other. Then we will need to ask what sort of tools and methodologies are available to would-be theologists  who seek to validate or falsify the existence of Deity/-ies and study/experience them to a greater degree, if It/They exist.
Here on Intelligent Universe, I have made initial explorations of two different concepts of "god," the "memetic" and the "cosmic." These two categories are not necessarily exhaustive, but they do seem to cover the two main types of gods found in human religions.
A "memetic god" exists as a "software persona" dwelling in a community of human hosts. It may be thought of as a human personality that has learned how to transmit itself from one human to another. Memetic gods think, act, and feel in recognizably human ways, and have human psychological needs and in some religions, physical needs to be met through sacrifices. An M-god can be recognized by its need for worshippers, and the importance to it of mechanisms for transferring it to other hosts, such as statues, oral traditions (myths), Scriptures, and so on.
A "cosmic" god is more abstract; inconceivably vast, "beyond human understanding," non-anthropomorphic, and linked either to the Cosmos or to some even greater "reality" that transcends Universe--or even renders it an illusion by comparison.
"Cosmic" gods are either impersonal, or their personalities consist of things such as “pure Awareness” “perfect Love” or other capitalized attributes that do not correspond exactly to their human counterparts. Examples of “cosmic” gods include the god of Deism, Brahmin from Hinduism, the god of Pantheism, Paul Tillich’s “Ground of Being,” and the “Cosmic” or “Christ Consciousness” of the New Age movement.
The gods of the Abrahamic religions (Judaism, Christianity, and Islam) seem to be a hybrid of the two, combining super-cosmic scale and assertions of non-anthropomorphic nature  with decidedly human motivations and needs, such as their urgent need to be obeyed and praised by their human subjects, exhibited in demands and behaviors that exactly mirror those of human kings and dictators.
Another approach to the subject of gods is the idea that accelerating advancement of technology will make it possible for humans to create godlike levels of intelligence, immortality, and power for themselves . This is a whole new spin on the cliché that “if God did not exist, it would be necessary to invent Him.” 
From this beginning, it may be possible to construct a genuine science of the divine. By “science,” I mean “a systematic effort to set in order the facts of experience,” which is not necessarily limited to the activities of people in lab coats with beakers and blackboards covered with equations, or the acceptance of caricatured assumptions such as “everything is the result of pointless, random collisions of material particles.” Forthcoming discussion will appear in the Comments section.
1. I use the term "theologist" to denote someone who studies gods in the same way a "biologist" studies life. In contrast, a "theologian" is someone whose job is to defend some particular orthodoxy against all comers. A "Christian theologian" cannot study the gods of ancient Egypt objectively any more than a "Muslim theologian" can objectively examine the Christian concept of God. A theologist is not bound this way, any more than a biologist is bound to consider only mammals as "true" life and all others (e.g. insects, fish, birds, plants) as "false" life.
2. Example: “’For my thoughts are not your thoughts, nor are your ways my ways,’” declares the Lord. ‘For as the heavens are higher than the earth, so are my ways higher than your ways, and my thoughts than your thoughts.’” --Isaiah 55:8-9
3. See Ray Kurzweil’s book, The Singularity is Near.
4. And Her.