Why is Khal Drogo willing to give Viserys an army in exchange for Daenerys?

To answer the question directly Drogo never intended to keep the deal with Viserys, at least that's how it is portrayed. He only appeared to want to marry Dany.

He's not willing to give Viserys the army, that might have been the initial deal but as you see throughout the series Viserys gets increasingly angry that Drogo has not given him his army yet.

VISERYS: When do I meet with the Khal? We need to begin planning the invasion.

ILLYRIO: If Khal Drogo has promised you a crown, you shall have it.

VISERYS: When?

ILLYRIO: When their omens favor war.

VISERYS: I piss on Dothraki omens. I waited 17 years to get my throne back.

_{Game of Thrones, Season 1 Episode 1, "Winter is Coming"}

Of course Drogo appears to have promised Viserys a crown and not an army; though the army was needed to get the crown. We find this out when Viserys finally gets it.

Viserys Targaryen: Tell him I want what was bargained for or I’m taking you back. He can keep the baby. I’ll cut it out and leave it for him.

Khal Drogo: (speaks Dothraki)

Viserys Targaryen: What’s he saying?

Daenerys Targaryen: He says yes. You shall have a golden crown, that men shall tremble to behold.

Viserys Targaryen: That was all I wanted. W-what was promised.

_{Game of Thrones, Season 1 Episode 6, "A Golden Crown"}

Of course Drogo only actually promises the army when Dany is almost killed and he promises this army to his son, not really to Dany.

Khal Drogo: Jorah the Andal, I heard what you did. Choose any horse you wish, it is yours. I make this gift to you.

And to my son, the stallion who will mount the world. I will also pledge a gift. I will give him the iron chair, that his mother's father sat upon. I will give him Seven Kingdoms. I Drogo, will do this. I will take my Khalasar west to where the world ends and ride wooden horses across the black salt water as no Khal has done before.

_{Game of Thrones, Season 1 Episode 7, "You Win or You Die"}

Tossing my thoughts into the ring:

Kahl Drogo wed Daenaerys because it increased his stature as a Kahl. No Kahl before him married someone who was in line to rule over a kingdom. If the Targaryan family did indeed return to the Iron Throne, by virtue of marriage, Drogo's influence, wealth, and power would increase exponentially.

And yes, she was a rare beauty with her fair skin and white/blond hair.

There's a few facts from the book that make the whole thing a bit clearer.

It is revealed that Varys and Illyrio have raised and trained someone called Aegon Targaryen, who would be the direct son of Rhaegar Targaryen, with a better claim to the throne than either Viserys or Daenerys. This plot has been ongoing since the fall of King's Landing, and the death of the Mad King

In addition, consider the following facts:

• Khal Drogo appears to have no intention of ever going West, and shared typical Dothraki beliefs on the sea and the lands across the sea.
• No real support was given to Daenerys or Viserys. Most of Dany's "education" comes from Viserys himself. Very little actual resources are provided to the pair.
• It is unclear that Viserys was ever respected by the Khals. Daenerys definitely had no actual authority except through indirect association with Drogo, until "Dragons happened".
• Everyone believes Aegon Targaryen, son of Rhaegar, was killed during the Sack of King's Landing. Everyone is aware that Viserys and Daenerys lived, and escaped to Essos.
• The prospect of Daenerys having a male child is one that causes many Lords to fear that the realm with bleed, as she could raise a generation of rebellions in order with the Blackfyres - who were only releases extinguished as a threat after like a century.
• Viserys does not speak Dothraki. Illyrio does. Illyrio treats with Khal Drogo on behalf of Viserys, and Illyrio benefits immediately as a result of the transaction selling Daenerys.

Given that, it is entirely plausible that Khal Drogo never agreed to give Viserys an army, or invade Westeros. He may not even be specifically lying to Viserys, or deceiving him, as we do not know the terms Khal Drogo made with Illyrio, and almost never communicates directly with Viserys. The one interaction I can think of is the actual crowning. Even after Viserys leaves to follow the khalasar to Vaes Dothrak, all his communication is filtered through Daenerys and Jorah Mormont.

• The one time Dany tries to convince Khal Drogo to go West, he responds in the negative. "The earth ends at the black salt sea", "No horse can cross the poison water". He doesn't even pretend to awareness of a deal to invade Westeros, but it is never directly asked either.
• Jorah Mormont reassures Viserys and Daenerys, but he was handed to them by Illyrio. He could be fully aware that there was never a deal to invade Westeros.

I think the underlying conclusion we are meant to achieve is that Viserys and Daenerys are somewhat of a False Flag operation. Westeros would be focused on the visible threats that they know of, expend resources to worry about and counter those threats, and be far less likely to be prepared for the real threat when it strikes.

It's when Robert sends an assassin, almost killing Daenerys, that Khal Drogo makes his sacred promise. He has now been personally affronted.

This is a little more murky in the show, but the personal benefit to Illyrio still checks out, and that makes all the points except the book spoiler relevant enough.