If we define "obvious prayer" as "direct appeal to the god" then you have three alternatives : the appeal may be indirect, the appeal may be to a proxy, or both. The differences between the three while real are mostly sophistry, in practice you are talking about adding indirection to avoid the "obvious prayer".
Instead of asking for what you want, you do something that results in the same effect. Henry Taylor gave some examples in his answer.
Basically you are taking advantage of either the personality of the god or some rule he follows. The rule might be a contractual obligation, a binding geas or precedent, or simply a result of some sort of a social dynamic between the divine powers. This works because the great power of the divine requires them to play by the rules to an insane degree to avoid breaking reality. Apparently rebuilding reality if you accidentally break it is a major pain and everybody involved will get really angry at the person responsible.
Use a proxy
Traditionally instead of asking the god for favor, you will form a pact or make a deal with a spirit or angel who has access to what you want. And with traditionally, I mean this is more or less how real world magic was supposed to work. Note that the difference between a spirit or angel powerful enough to provide useful magic and an actual god is largely theoretical. A polytheist will consider them lesser gods, a monotheist will see them as lesser beings or extensions of the power of God.
The proxy may also be an object or a place associated with the divine to the point it has actual power. With the divine the "object" may be an immaterial thing, the difference between material and immaterial things is really a mortal limitation. As far as a god is concerned the verbal promise he made to your ancestor six thousand plus years ago is more real and concrete than the mountain your castle is built on.
The proxy can also be a person or bloodline. It can even be a nation, an ideal, or an organization.
Spirits and angels are just as rule bound and for the same reasons as actual gods. Objects and places may respond to reproductions or invocations of the circumstance that imbued them with power. If the power was imbued on purpose, it may respond to anything the one making it wanted it to respond. This is typically the case if the proxy is a divine promise or pact.