'engender support' is correct and usable in written English.
It is used to express the idea of gaining someone's support through persuasive action. For example, "The leader's passionate speech was able to engender support for the cause from the audience."
City agencies often predict doom and gloom to engender support only to have the situation turn out better than anticipated.
Mr. Doctoroff has already met many of the 125 voters, trying to engender support and trust through his warm, personable approach.
It might receive a very rare generous alumni gift, spend it wisely, and so engender support from generations of future alumni.
Doing so has the potential not only to engender support for protecting native species, but also to enhance human well-being.
Findings have implications for coalition building as advocates may engender support for green energy policy by framing sanctions as protecting natural commons, and framing subsidies either in this same way and/or as producing benefits for communities.
Not the entire bill mind you, just one piece that was included to engender support from Republicans.
But save your nostalgia; familiarity here breeds contempt as much as it engenders support.
A more modest fiscal program founded along cost-benefit lines would have engendered support from at least some of the most vocal critics of the ARRA.
The extreme consequences of untreated and undetected perinatal depression (suicide and infanticide; Lusskin et al. 2007) have awakened public interest and engendered support for second trimester screening.
Although Doug Jones is a moderate candidate who has had some success in Alabama and might engender some support, especially with the backing of Vice President Joe Biden, who intends to campaign for him, and although he'd undoubtedly be a strong senator, the Democratic Party must immediately urge him to withdraw from the race and replace him on the ballot with Luther Strange.
Mr. Gore has failed to engender deep support from many past backers.
