Sending as gifts
I found a clear statement that you do in fact owe gift tax for gifts made to foreign people (foreign from the perspective of the United States government). There is a $15,000 gift tax exclusion per person per year in 2019. That would be per parent, so you could send $30,000.
If you are married, you and your spouse could each send that amount. So $60,000 if you are married but only $30,000 if you are not.
If your parents are open to having other people on the deed, you could send $15,000 ($30,000 if married) to each person on the deed. You can also send $15,000 ($30,000 if married) to spouses not on the deed (e.g. if you have a sister whose name is on the deed, you could send to both her and her husband).
If we were closer to the end of the year, you could send $15,000 this year and then another $15,000 next year. But I don't know that that helps you. Mentioning for future readers.
If you send more than the limit, you have to file Form 709 saying that you are using part of your estate exemption. That exemption is $11,400,000 in 2019. If your estate is likely to be smaller than this, this might be the simplest method. Just send $15,000 to one parent and the remainder to the other. Your remaining estate tax exclusion would be around $11,350,000.
If you send money to other people with the idea that those people will then gift the money to your parents, that would be tax evasion. If they caught you, they would charge you penalties, even though you won't owe any immediate tax.
If you are on the deed, you could send the whole $80,000. Because then it is simply you buying a property, possibly with partners. The relevant section from the IRS:
What is considered a gift?
Any transfer to an individual, either directly or indirectly, where full consideration (measured in money or money's worth) is not received in return.
Being on the deed as an owner of $80,000 worth of the property would be the "full consideration" mentioned.
It's unclear if the $80,000 is the full value of the property or not. If it is, then you would be the sole owner. If not, you would share ownership.
If there is income from the property, you might have to report it in the US. You might have to file Form 1116 to get credited for tax paid in India. But if there is no income, that's not a problem.
If your parents would leave you the property in their will anyway, this would allow you to avoid paying inheritance tax from them.