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...
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.
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.
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).
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.
It's unlikely, but up to your DM
There are guidelines for tweaking backgrounds in the Player's Handbook (PHB), which allow you to customize backgrounds (or create a new one) if the current ones aren't to your liking. They state:
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. (PHB, p. 125, bold added)
The rules go out of their way elsewhere to clarify that two skill proficiencies shouldn't stack. For example:
Your proficiency bonus can’t be added to a single die roll or other number more than once. (PHB, p. 12)
If a character would gain the same proficiency from two different sources, he or she can choose a different proficiency of the same kind (skill or tool) instead. (PHB, p. 125)
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. (PHB, p. 173)
All these rules suggest that you can't just chose the same proficiency twice, and stack your bonuses.
Expertise in deception might not unbalance the game too much. Whether or not someone believes you depends on more than how convincingly you lie (you could sound completely sincere when you tell someone that you are a two inch tall pink bunny, but if they are looking right at you they'll still be hard to convince). But the ability stack proficiencies into one skill in general could definitely unbalance the game, especially if it was allowed more than twice.
Even if you only grant expertise, there are still issues at hand. A key example would be allowing a Fighter or Paladin to gain expertise in Athletics. The classes that gain expertise (Rogues and Bards) tend to rely on dexterity for their AC calculations, and thus to prioritize dexterity over strength as an attack ability. If a character with a high strength could gain expertise in athletics without multiclassing (or requiring a high dexterity or charisma), then their ability to grapple or shove opponents would be extremely hard to resist. Such an advantage should cost quite a lot more than the loss of a single skill proficiency. And backgrounds like the one you propose open the door to this kind of tweaking.
A background provides part of the "backstory" for your character: it's the non-adventurer life they had before they decided to pursue their current path. Typically, a background describes a lifestyle that someone may pursue for a long time, and could describe a profession or calling you pursued. Usually, it explains how you survived and thrived before now: what earned you a roof above your head, and put food on your plate.
It's very rare for a person's livelihood to be based on only one skillset. A blacksmith needs to be skilled with their tools, but they also have to be skilled at sizing up customers and negotiating prices (hence Guild Artisan's proficiencies in Insight and Persuasion, as well as their artisan's tools). A con-man must be able to convince others of their lies, but they also may need to steal identification off of unsuspecting nobles, or forge documents (thus a Charlatan's proficiency in Slight of Hand and Forger's Tools, as well as Deception). In general, even if your background relied heavily on one of your skills, it also required you to become at least competent in another one.
Giving yourself a background with expertise in Deception, but no other skill proficiency, suggests that all your character ever learned to do as an acolyte is lie. But didn't they also need to learn the stories of their deity, or the laws of their religion (and thus become proficient in Religion)? Or if he learned of his deity on the street without formal teaching, and thus never studied religion, didn't he need to find a place to sleep at night, and learn where to forage for food (and thus become proficient in Survival)?
Whatever story you chose for your background, it's unlikely that story relied on your character doing one thing, and one thing only.
But... DM's call
Ultimately, any alteration to an existing background (or to any of the given rules) is up to your DM. But keep the above concerns in mind before you propose such a change.