Technically, jutky is correct: once the Great Sanhedrin moved out of their office in the Beis Hamikdash, forty years before it was destroyed, capital punishment was no longer carried out. (Shabbos 15a, et al)
That said, we do find sporadic cases where a beis din executed someone judicially in later times. One is in Sanhedrin 52b, where a kohen's daughter who committed adultery was executed by burning (as per Lev. 21:9), though Rav Yosef there points out that this was in fact the wrong thing to do.
The Rosh, in his responsa (17:8), discusses a case where the beis din of Cordova wanted to execute someone for blaspheming G-d, and asked him whether this was the correct thing to do. He writes:
הפלאתם לשאלני בדיני נפשות כי בכל
הארצות ששמעתי עליהם אין דנין דיני
נפשות לולי פה בארץ ספרד ותמהתי מאד
בבאי הלום איך היו דנין דיני נפשות בלא
סנהדרין ואמרו לי כי הורמנא דמלכא הוא.
וגם העדה שופטים להציל כי כמה דמים היו
נשפכים יותר אם היו נדונים ע"י גוים
והנחתי להם כמנהג' אבל מעולם לא הסכמתי
עמהם על איבוד נפש
"You surprise me by asking about a capital case. In all of the countries that I have heard of they do not judge capital cases, except here in Spain. When I arrived here I was most astonished how they could judge such cases without a Sanhedrin; I was told that this is by permission of the king, and also that the beis din's judgment saves lives, since much more blood would be spilled were they [Jews accused of crimes] to be judged by non-Jews. So I allowed them to continue their custom; but I have never agreed with them about taking life."
Though in this case he tells them that because of the severity of the sin - indeed, the non-Jewish authorities also treated such actions harshly - they could go ahead and do whatever they see fit (his own recommendation was to remove the fellow's tongue).
The testimony mentioned in this responsum is dated "Sunday, 16 Adar, 1358 according to the non-Jewish count" - which I believe refers to the Spanish Era, since the Rosh was no longer living in 1358 CE. This would place the event in 1321. So we see that at least as late as that date, batei din in Spain were carrying out judicial executions.