@Parda3: For short term stay i.e less than 3 months period: Please follow this link to receive travel authorization from Srilanka government. This can be done online. Once we have this travel authorization and arrive at the airport, they issue visit visa for 1 month that can be extended to 5 more months maximum. https://eta.gov.lk/etaslvisa/etaNavServ?payType=1
For long term stay i.e more than 3 months period: Please let the monastery know about your plan for a long term stay. They will process your case to immigration department and issue a letter of sponsorship which you need to show to immigration department once arrive. This way the visa can be extended in the future for many years.