Q:

Could you grant 1 expertise instead of 2 proficiencies for Background?

I wanted to make a follower of Cyric,the God of lies. Would it be unreasonable to give him expertise in deception, so he becomes better at lying? The thing about it is that he would lose out on other things...

A:

Definitely not by RAW
The Player's Handbook does not permit your proficiency bonus to ever be added more than once to a roll, explained explicitly in Chapter 7, when explaining your Proficiency Bonus:

Your proficiency bonus can't be added to a single die roll or other number more than once. For example, if two different rules say you can add your proficiency bonus to a Wisdom saving throw, you nevertheless add the bonus only once when you make the save.
Occasionally, your proficiency bonus might be multiplied or divided (doubled or halved, for example) before you apply it. For example, the rogue's Expertise feature doubles the proficiency bonus for certain ability checks. If a circumstance suggests that your proficiency bonus applies more than once to the same roll, you still add it only once and multiply or divide it only once.

A few reasons not to allow this
The biggest reason not to allow this is because it intrudes on the features that Rogues and Bards have. Their notable class features include the ability to gain Expertise on several skills of their choice; having this option be open to any character who chooses to forgo their other background-provided skills would make those classes less powerful and devalue Expertise as a feature.
5e also has a strong design intent called "Bounded Accuracy", whereby modifiers and bonuses are, as much as possible, crunched into smaller spaces. Giving every character potential access to the Expertise feature interferes with this design principle.
Ask your DM
If your DM is fine with it, then they can permit it. I wouldn't recommend allowing it, but if they're alright with it, then go for it.

A:

You can replace one of the skills with Deception using a custom background
The Player's Handbook describes the method for creating custom backgrounds as follows:

You might want to tweak some of the features of a background so it better fits your character or the campaign setting. To customize a background, you can replace one feature with any other one, choose any two skills, and choose a total of two tool proficiencies or languages from the sample backgrounds.

So if you are an Acolyte of Cyric, it may be more fitting to have Insight and Deception rather than Insight and Religion (or some other swap). This is perfectly within the realm of the rules and gives you that better at Deception flavour.
Expertise?
Granting expertise, or more accurately: doubled proficiency, would be a separate feature entirely. It is not within the rules to replace one of the skill proficiencies granted by a background with a doubled proficiency. While we do have one example of a background with only 1 skill proficiency, we don't have enough precedent to know what that skill proficiency could be replaced by. 
As such, you would have to ask your GM (as Baron's answer describes) for a customized Background feature to replace Shelter of the Faithful, but keep in mind the implications that has on other features where expertise serves as part of a class identity (that Xirema's answer discusses).

A:

If the DM allows it, you can create any background features you want.
Page 126 of the Player's Handbook has a section titled Customizing A Background. In particular, it states this:

If you can't find a feature that matches your desired background, work with your DM to create one.

There is no base background that will provide expertise on deception. However, given that D&D is a roleplaying game and as a result having a character with a background you find interesting is important to the game, it's flexible. Speak to your DM and explain your character, then ask if this adjustment would be acceptable to him or her.

