Istijmaar is valid whether one uses stones or tissue paper, even if water is available; there is no difference of opinion among the scholars on this point.
The evidence that istimaar using stones and the like is acceptable is the report narrated by al-Bukhaari (159) and Muslim (237) from Abu Hurayrah (may Allaah be pleased with him), which says that the Messenger of Allaah (peace and blessings of Allaah be upon him) said: “Whoever does wudoo’, let him rinse his nose, and whoever does istijmaar let him use an odd number.”
Ibn al-Qayyim (may Allaah have mercy on him) said in Ighaathat al-Lahfaan (1/151) that there is consensus among the Muslims that it is permissible to do istijmaar using stones both in the winter and in the summer.
When doing istijmaar using stones, it is stipulated that one should wipe three times or more in order to clean the place properly. That is because Muslim (262) narrated that Salmaan al-Faarisi (may Allaah be pleased with him) said: “The Prophet (peace and blessings of Allaah be upon him) forbade us to clean ourselves using less than three stones.”
Doing istinja’ with water is better, because of the report narrated by Muslim (271) and al-Nasaa’i (45) from Anas ibn Maalik (may Allaah be pleased with him) who said: When I was a boy, when the Messenger of Allaah (peace and blessings of Allaah be upon him) entered the toilet I would carry a small vessel of leather filled with water, and he would clean himself with water.
Ibn Qudaamah (may Allaah have mercy on him) said in al-Mughni (1/206):
If a person wants to do just one of them, then using water is better, because of the hadeeth that we have narrated, and because it purifies the place and removes the dirt itself and its traces, and is more cleansing.
But limiting oneself to stones only is sufficient, and there is no difference of opinion among the scholars concerning that, because of the reports that we have mentioned and because that is the consensus of the Sahaabah (may Allaah be pleased with them).
And Allaah knows best.