1) Believable 2) Credible 3) Dewy-eyed 4) Easily convinced 5) Gullible 6) Illogical 7) Irrational 8) Naif 9) Naive 10) Overcredulous 11) Trustful 12) Trusting 13) Unquestioning 1) Credible 2) Gullible 3) Naif 4) Naive 5) Overcredulous 6) Trustful 7) Trusting 8) Unquestioning 9) Unsuspecting 
• (a.) Apt to believe on slight evidence; easily imposed upon; unsuspecting. • (a.) Believed too readily.
Cred'u·lous adjective [ Latin credulus , from credere . See Creed .] 1. Apt to believe on slight evidence; easily imposed upon; unsuspecting. Landor. « Eve, our credulous mother. Milton. » 2. Believed too readily. [ Obsolete] ...
ready to believe things 
[adj] - showing a lack of judgment or experience 2. [adj] - disposed to believe on little evidence
credulous, credulousness 1. Ready or too easily disposed to believe. 2. Overly ready to believe; apt to believe on weak or insufficient grounds. 3. Someone is credulous when he or she is all too ready to believe something or someone.
adjective showing a lack of judgment or experience; `so credulous he believes everything he reads`
willing to believe or trust too readily, esp. without proper or adequate evidence; gullible. · marked by or arising from credulity: a credulous rumor.