There is only one direct train from Madagaon Junction (In Goa) to Jaipur Junction.
Train Name: Marusagar Express
Train No. 2977 (With effect from 20-12-2010 it will be changed to ⇒12977)
It is a weekly train (Leaves originating station Ernakulam Junction [in Kerala) on Fridays) Leaves Madgaon on Saturdays and reaches Jaipur on Sunday.
1865 Km, about 29 Hours journey, 12 major halts between Jaipur Junction and Madgaon Junction.
Fare for Indian citizens:
AC 3-tier Rs. 1330/-
AC 2-tier Rs. 1822/-
AC 1st Class Rs. 3085/-
For more details and particulars about fare, seat availability, etc:
http://indiarailinfo.com/train/1068/272/511/1
For route map:
http://indiarailinfo.com/train/map/1067/511/272
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Alternatively you can travel up to Mumbai and change over to Jaipur
For Madgaon to Mumbai:
http://indiarailinfo.com/search/511/466?kkk=1287329903953
For Mumbai to Jaipur:
http://indiarailinfo.com/search/466/272?kkk=1287330095171
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Indian Railways Official website:
http://www.indianrail.gov.in/
Online Train reservation and related info:
http://www.irctc.co.in/
International tourists info:
http://www.indianrail.gov.in/international_Tourist.html