Cover is gained in one of two ways: via Pact, or via Angel-Jacking. Both are detailed in DtD, page 116, and Flowers of Hell: the Demon's Player's Guide, page 30.
There are a couple ways to look at costs, but no clear "cheapest" method:
When an Angel-Jacking may be advantageous:
If the Cover being created is fairly low (eg, 2 dots), and the Demon has high Resolve and Primum, it could only take a single roll to get two successes (with the opposing Angel getting less than 2.) This could even benefit from teamwork, but it also requires other dice rolls, "left to the Storyteller to determine on a case-by-case basis."
When a Soul Pact may be advantageous:
Pacts can be generated through roleplay alone; depending on the ST, there may be no roll to convince the victim. There is a mandatory 1 Dot of Willpower to be spent; to "buy it back" to the character's sheet costs at least 1 Dot of Experience.
When a Patch Job may be advantageous:
A Cover created through a patch job would have to cost at least 3 Cover Experience (3 CE per dot * 1 dot.) It'd be very, very fragile, but, if the intention is to burn it fairly quickly, that might not make much of a difference. The bargaining for a small Pact might be even easier, from a roleplay perspective - or a roll to convince the pactee (eg, Manipulation + Persuasion) might get a bonus, at the ST's discretion.
The trick to Covers via Pacts is that, while the Soul Pact's cost has a smaler magnitude, non-Cover Experience can be used on more items, making it a more "valuable" currency.
Ultimately, the best minimum steps for a "disposable" Cover vary on circumstance, but it's worth pointing out that FoH calls out Patch Job Covers as "...well suited to 'one-and-done' operations. ...If the operation goes badly, going loud is always an option - and at least you aren't burning a Cover that's had a lot of effort sunk into it."