There is a way to find out all the base learners supported by AdaBoostClassifier. A compatible base learner's fit method needs to support sample_weight, which can be obtained by running following code:
from sklearn.utils.testing import all_estimators
for name, clf in all_estimators(type_filter='classifier'):
if 'sample_weight' in inspect.getargspec(clf().fit):
AdaBoostClassifier, BernoulliNB, DecisionTreeClassifier, ExtraTreeClassifier, ExtraTreesClassifier, MultinomialNB, NuSVC, Perceptron, RandomForestClassifier, RidgeClassifierCV, SGDClassifier, SVC.
If the classifier doesn't uses predict_proba, you will have to simply set AdaBoostClassifier parameter algorithm = 'SAMME'.
To learn more about Adaboost, go through Machine Learning Course. Also, visit Machine Learning Tutorial to master the course.
Hope this answer helps you!