There are countries that you cannot become a citizen if you have no blood or religious relation to the country.
The most difficult, a few
The Gulf countries are extremely strict. The UAE for example requires 20 years to qualify, to be a Muslim and have locals back you up. Very few foreigners actually receive it.
Monaco requires 10 years of residence, but ultimately the prince has to agree for you to become his subject.
Andorra requires 20 years of residence, Liechtenstein demands a massive 30 years of residence although you can be voted citizen by the community after 10 years of permanent residence. San Marino is also 30 years and 2/3 of approval from the general council.
There are more places like Brunei or small jurisdictions that make it close to impossible also.
You could say Israel if you are Jewish or other countries if apply by descent or marriage.
For naturalization you have the Citizenship by investment schemes that enable you to obtain a passport by donating money to a government. In term of fastest, from application to passport: Dominica, Grenada, Cyprus, Comoros, Vanuatu and St Lucia can be obtain in roughly 3 months. There are a lot more citizenship you can obtain by investment go to this link:
In regular citizenship Panama citizenship can be obtain after 1 year of Permanent residency if you are from an Hispanic country of origin.
Mauritius also after 2 years of permanent residence, which you can obtain by investing.
Singapore take 3 years after Permanent Residence.
Russia 3 years, down to 2 years for ex USSR citizens.
Others are Canada, the USA, Uruguay….. Latin American give the citizenship pretty fast after becoming permanent resident, but becoming a permanent resident cant take 2–3 years.