I think using the TCGA data is the best option as you get many samples with miRNA and mRNA expression. Check the following link to download the relevant data (i.e. Expression-Genes and Expression-miRNA). If you prefer miRNA microarray data, you can use data from Glioblastoma (GBM) or Serous Cystadenocarcinoma (OV), because you get expression through sequence data for other cancer types.

https://tcga-data.nci.nih.gov/tcga/dataAccessMatrix.htm

You can use starBase Pan-Cancer Analysis Platform. starBase Pan-Cancer Analysis Platform is designed for deciphering Pan-Cancer Networks of lncRNAs, miRNAs, ceRNAs and RNA-binding proteins (RBPs) by mining clinical and expression profiles of 14 cancer types (>6000 samples) from The Cancer Genome Atlas (TCGA) Data Portal (all data available without limitations).

starBase generated Pan-Cancer networks of CLIP-Seq experimentally supported miRNA-lncRNA and miRNA-mRNA interactions.

Pan-Cancer miRNA-mRNA interactions can be available at http://starbase.sysu.edu.cn/targetSite.php