The best replacement for needy is clingy.

The best alternatives to needy are rated as following:
★★★★★  clingy
★★★★  greedy
★★★  vulnerable
★★★  having needs
★★  lonely
★★  affectionate
★★  needed
★  desperate
★  high maintenance
★  neediest
★  needier

Your alternative for needy is not listed? Suggest!
Speaking about needy, one probably shouldn't forget about being needy.

Other search terms related to needy and their ratings are:
★★★★★ being needy
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Google Trends

Scale is based on the average worldwide traffic of needy in all years. Click on graph for more.
needy
clingy
greedy